Problem Solving on Permutations & Combinations

Out of 5 consonants and 4 vowels, how many words of 2 consonants and 2 vowels can be formed?

• 1400
• 1420
• 1440
• 1460

In a group of 5 boys and 4 girls, three children are to be selected. In how many different ways can they be selected such that at least two girls should be there?

• 44
• 34
• 24
• 14

In how many different ways can the letters of the word 'ENGINEERING' be arranged so that the vowels always come together?

• 400
• 500
• 600
• 700

There are 6 men and 5 women and you need to form a committee of a man and a woman. In how many ways can the committee be formed?

• 30
• 36
• 40
• 64

In how many ways can the letters of the word 'AUGUST' be arranged?

• 120
• 240
• 360
• 480

How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 if repetition of digits is not allowed?

• 100
• 120
• 200
• 340

An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair?

• 100
• 80
• 110
• 64

In how many ways can 5 persons be arranged in a row such that 3 particular persons should always be together?

• 100
• 50
• 36
• 16

How many 8 digit mobile numbers can be formed if any digit can be repeated and 0 can also start the mobile number?

• 10⁸
• 10⁷
• 10⁶
• 10⁵

How many numbers not exceeding 10000 can be made using the digits 2,4,5,6,8 if repetition of digits is allowed?

• 9999
• 820
• 780
• 740