If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E ?

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen ?

In how many ways can the letters of the word PERMUTATIONS be arranged if the (i) words start with P and end with S,

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

If $frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}$, find $x$.

In how many of the distinct permutations of the letters in MISSISSIPPI do the four $I$'s not come together?

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible ?

Compute $frac{8!}{6! \times 2!}$

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated ?

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (i) exactly 3 girls ?

Find $n$ if ${}^{n–1}P_3 : {}^nP_4 = 1 : 9$.

In how many ways can the letters of the word PERMUTATIONS be arranged if the (ii) vowels are all together,

Evaluate $frac{n!}{(n-r)!}$, when (ii) $n = 9, r = 5$.

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position?

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (ii) atleast 3 girls ?

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

How many 4-digit numbers are there with no digit repeated?

In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions ?