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If eleven member of a committee sit at a round table so that the President and Secretary always sit together, then the number of arrangements is

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Important Questions on Number Systems

EASY
The number of ways, in which 5 girls and 7 boys can be seated at a round  table so that no two girls sit together is
EASY
Find the number of ways of preparing a chain with 6 different coloured beads.
EASY
The number of ways 5 boys and 5 girls can be seated at a round table, so no two boys are adjacent is _____
EASY
The sum of the digits in the unit's place of all the 4 - digit numbers formed by using the numbers 3, 4, 5 and 6, without repetition is :
HARD
Six persons A, B, C, D, E and F are to be seated at a circular table facing towards the centre. Then the number of ways that can be done if A must have either E or F on his immediate right and E must have either F or D on his immediate right, is
EASY
The total number of permutations of n(>1) different things taken not more than r at a time, when each thing may be repeated any number of times is
MEDIUM
A round table conference is attended by 3 Indians, 3 Chinese, 3 Canadians and 2 Americans. Find the number of ways of arranging them at the round table so that the delegates belonging to same country sit together.
MEDIUM
The number of four-letter words that can be formed with letters a, b, c such that all three letters occur is
MEDIUM
20 persons are invited for a party. The number of ways in which they and the host can seated at a circular table, if two particular persons be seated on either side of the host is equal to
EASY
The number of ways that a circle can be made out of 6 black and 4 white men standing on a ring, so that all the white men come together is
MEDIUM
The number of four-digit numbers strictly greater than 4321 that can be formed using the digit 0,1,2,3,4,5 (repetition of digits is allowed) is:
MEDIUM
If f=13   24   36    47   55   61S6 then f-1 is
EASY
The number of 6 digit number that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is:
MEDIUM
Two girls and four boys are to be seated in a row in such a way that the girls do not sit together. In how many different ways can it be done?
HARD
If all the seven letters of the word LEADING are permuted in all possible ways and the words thus formed are arranged as in the dictionary order, then the word in 2017th place is
MEDIUM
5 boys of class VI6 boys of class VII and 7 boys of class VIII sit in a row. The number of ways they can sit so that boys of the same class sit together is
MEDIUM
In a group of 8 girls, two girls are sisters. The number of ways in which the girls can sit so that the two sisters are not sitting together is
EASY
The number of ways in which 6 men and 5 women can sit at a round table if no two women are to sit together is given by
HARD
Five persons A, B, C, D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then the number of ways of distributing the hats such that the persons seated in adjacent seats get different coloured hats is
MEDIUM
The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular girl G1 never sit adjacent to each other, is: