Quiz on Combinatorics and Arrangements

From a group of 8 men and 7 women, six persons are to be selected to form a committee so that at least 4 men are there on the committee. In how many ways can it be done?

• 1850

• 756

• 1890

• None of these

In how many different ways can the letters of the word 'COMPUTER' be arranged in such a way that the vowels always come together?

• 720

• 4330

• 4320

• None of these

Out of 8 consonants and 5 vowels, how many words of 4 consonants and 3 vowels can be formed?

• None of these

• 700

• 710

• 1716

How many 3-digit numbers can be formed by using the 6 digits 2,3,4,5,6,8 if the number is to be odd and repitions are not allowed?

• 80

• 216

• 20

• 120

A bag contains 5 red marbles and 6 white marbles. Find the number of ways that 4 marbles can be drawn from the bag if 4 marbles must be of the same colour.

• 15

• 5

• 75

• None of these

If there are 3 cars and 4 motor cycles, how many ways the vehicles be parked in a line such that cars and motor cycles alternate each positions?

• 70

• 144

• 35

• 288

A book shelf has N fiction books and 6 non fiction books. If there are 150 ways to choose 2 books of each type, how many fiction books are there on the shelf?

• 8

• 6

• 5

• 7

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is

• 40

• 60

• 80

• 100

If repetition of the digits is allowed, then the number of even natural numbers having three digits is

• 500

• 450

• 100

• 125

All the letters of the word 'BASIC' are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is

• 144

• 36

• 18

• 120