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Number of ways in which 4 objects out of 6 distinct objects can be deranged are

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Important Questions on Permutation and Combination

MEDIUM
Mathematics>Algebra>Permutation and Combination>Derangements
The number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words are written as in a dictionary, then the 50th word will be
MEDIUM
Mathematics>Algebra>Permutation and Combination>Derangements
A person writes letter to six friends and addresses the corresponding envelopes. Let x be the numbers of ways so that at least two of the letters are in wrong envelopes and y be the numbers of ways so that all the letters are in wrong envelopes. Then x-y=
EASY
Mathematics>Algebra>Permutation and Combination>Derangements
There are 7 greeting cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly 4 of the cards go into envelopes of respective colour is,
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Mathematics>Algebra>Permutation and Combination>Derangements
Six persons P, Q, R, S, T and U were sitting around a hexagon table facing the centre. U was sitting opposite to P, who was the immediate left of R. S was sitting to the immediate right of U, and T was exactly between P and S. What was the sitting ocation of Q?
HARD
Mathematics>Algebra>Permutation and Combination>Derangements
Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and more over the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is
HARD
Mathematics>Algebra>Permutation and Combination>Derangements
We will say that a rearrangement of the letters of a word has no fixed letters if, when the rearrangement is placed directly below the word, no column has the same letter repeated. For instance, HBRATA is a rearrangement with no fixed letters of BHARAT. How many distinguishable rearrangements with no fixed letters does BHARAT have? (The two A's are considered identical)
MEDIUM
Mathematics>Algebra>Permutation and Combination>Derangements
If all possible numbers are formed by using the digits 1, 2, 3, 5, 7 without repetition and they are arranged in descending order, then the rank of the number 327 is
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Mathematics>Algebra>Permutation and Combination>Derangements
Six boys P, Q, R, S, T, and G are sitting around a circular table facing towards the centre (not necessarily in the same order). P is to the immediate right of G. Q is second to the left of T. R is second to the left of S. G is second to the right of S. How many boys are sitting between R and T?
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Mathematics>Algebra>Permutation and Combination>Derangements
Six buses B1, B2, B3, B4, B5 and B6 are parked around a circular path (not necessarily in the same order). B3 is third to the right of B6. B4 is to the immediate Left of B1. B2 is second to the left of B6. How many buses are between B5 and B1?
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Mathematics>Algebra>Permutation and Combination>Derangements
Six people are sitting in a circle. 'J' is between 'N' and 'O'; 'N' is opposite 'M'; and 'L' is not in either of the neighbouring seats of 'N'. Who is opposite to 'K'?
MEDIUM
Mathematics>Algebra>Permutation and Combination>Derangements
If there are 5 letters written to 5 different people and 5 envelopes addressed to them, then the number of ways in which these letters can be arranged so that no letter goes into its corresponding envelope is
MEDIUM
Mathematics>Algebra>Permutation and Combination>Derangements
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:
EASY
Mathematics>Algebra>Permutation and Combination>Derangements
Six employees R1, R2, R3, R4, R5, and R6are sitting around a circular table facing towards the centre (not necessarily in the same order). R5 is third to the left of R3. R2 is to the immediate left of R4. R1 is to the immediate left of R5. Which of the following statement is incorrect about R6?
MEDIUM
Mathematics>Algebra>Permutation and Combination>Derangements
A dictionary is printed consisting of 7 letters words only that can be made with a letters of word CRICKET. If the words are printed at the alphabetical order as in an ordinary dictionary, then the number of words before the word CRICKET is
EASY
Mathematics>Algebra>Permutation and Combination>Derangements
Six boys R, L, B, T, W and N are standing in a row facing towards north (Not necessarily in
the same order). Two boys are standing between R and N. T is standing to the immediate
left of R. L is standing second to the left of B. W is third to the right of B.
Who is standing to the immediate right of R?
EASY
Mathematics>Algebra>Permutation and Combination>Derangements
Five advocates G, N, M, L and A are sitting around a circular table facing towards the centre (not necessarily in the same order). A is sitting between G and L. M is second to the right of L. G is towards the immediate left of A. Who is sitting second to the left of A?
EASY
Mathematics>Algebra>Permutation and Combination>Derangements
Five pens D, E, F, G and H are kept one above the other (not necessarily in the same order). Only H is between E and F. F is below E. G is just below F. D is three places below H. How many pens are between E and D ?
HARD
Mathematics>Algebra>Permutation and Combination>Derangements
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is.....
HARD
Mathematics>Algebra>Permutation and Combination>Derangements
If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is 
EASY
Mathematics>Algebra>Permutation and Combination>Derangements
In a March Past, seven persons are standing in a row, Q is standing left to R but right to P. O is standing right to N and left to P. Similarly, S is standing right to R and left to T. Find out who is standing in the middle.