1000+ Permutations and Combinations Questions and Answers - 1

Ans: D

6 letters of the word PRAISE can be arranged in 6! ways = 720 ways.

Ans: B

The word ALLAHABAD has 9 letters in all. The letter A occurs 4 times, the letter L occurs 2 times and the remaining three letters H, B, D each occur once.

= $${9!} /{4! 2! 1! 1!}$$

= $${9 × 8 ×7 × 6 × 5 × 4!} / {4! × 2}$$

= 9 x 8 x 7 x 3 x 5 = 7560.

Ans: C

Any number between 1000 and 10000 is of 4 digits. The unit’s place can be filled up by 4 or 5 or 6, that is, in 3 ways.

Similarly, the ten’s place can be filled up by 4 or 5 or 6 that is, in 3 ways. The hundred’s place can be filled up by 4 or 5 or 6, that is in 3 ways and the thousand’s place can be filled up by 4 or 5 or 6, that is, in 3 ways.

Hence, the required number of numbers = 3 x 3 x 3 x 3= 81.

Ans: C

Each of the first 3 questions can be answered in 4 ways.

Each of the last 3 questions can be answered in 5 ways.

By, the fundamental principle of counting, sequences of answers are

4 × 4 × 4 × 5 × 5 × 5 = 64 × 125 = 8000.

Ans: A

The first event of going from Delhi to Mumbai can be performed in 15 ways as he can go by any of the 15 buses. But the event of coming back from Mumbai can be performed in 14 ways (a different bus is to taken).

Hence, both the events can be performed in 15 × 14 = 210 ways.