G Tewani Solutions for Chapter: Permutation and Combination, Exercise 2: DPP

The number of different words that can be formed using all the letters of the word $\mathrm{SHASHANK}$ such that in any word the vowels are separated by at least two consonants, is

The number of ways in which six boys and six girls can be seated at a round table so that no two girls sit together and two particular girls do not sit next to a particular boy is

Six cards are drawn one by one from a set of unlimited number of cards, each card is marked with numbers $-1, 0$ or $1$. Number of different ways in which they can be drawn if the sum of the numbers shown by them vanishes, is

The total numbers formed from a positive six-digit number which is divisible by $9$ and whose four digits are$1,0,0,5$, is

Number of nine-lettered words that can be formed using all the letters of the word $\text{'}\mathrm{MEENANSHU}\text{'}$, if alike letters are never adjacent, is

Number of ways in which the letters of the word $ABBCABBC$ can be arranged such that the word $ABBC$ does not appear in any word, is

The number of $4$ digit natural numbers such that the product of their digits is $12$, is

A class has three teachers, $Mr. X$, $Ms. Y$ and $Mrs. Z$ and six students $A, B, C, D, E, F$. Number of ways in which they can be seated in a line of  $9$ chairs, if between any two teachers there are exactly two students, is