Permutation and Combination Questions

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then, the number of words which have at least one letter repeated, is...

Number of divisors of the form (4n + 2), n ≥ 0 of the integer 240 is

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such a...

The number of five digit numbers that can be formed using all the digits 0, 1, 3, 6, 8 which are -

Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1 - Tn = 10, then the value of n is :...

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from10 white, 9 green and 7 black balls is :-...

The total number of ways in which 5 balls of different colors can be distributed among 3 persons so that each person gets at least one ball is

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total savi...

The value of the expression $^{47}C_4 + \displaystyle\sum_{j=1}^{5} {}^{(52-j)}C_3$ is equal to

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose chairs from among those marked 1 to 4, and then the men select chairs from among the re...

A five digits number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is

An n digit number is a positive number with exactly n digits. Nine hundred n- digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of n for ehich this is possible,...

How many dofferent nine digit numbers can be formed form the number 22 33 55 888 by rearranging its digis so that the odd digits occupy even positions

Tne number of arrangements of the lettrs of the word BANANA in which the two N′s do not appear adjacently, is

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of...

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

Find the number of ways to distribute 8 identical balls among 3 distinct boxes such that none of the boxes remains empty.

If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr + 1 + nCr-1 + 2 × nCr equals...

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is...