SSC CGL (Prelims) General: Permutation and Combination questions with solutions

Q1. In a room of 8 people, how many different handshakes are possible if each person shakes hands once with every other person?

1. 21
2. 24
3. 28
4. 32

Answer: 28

Each handshake is a unique pair of people. The number of pairs among 8 people is ${8 \choose 2} = \frac{8\times7}{2} = 28$.

Q2. How many meaningful 4-letter English words can be formed using the 2nd, 3rd, 4th, and 5th letters of the word TEACHER, without repetition?

1. Two
2. Four
3. One
4. Three

Answer: Two

The 2nd, 3rd, 4th, and 5th letters of TEACHER are E, A, C, and H. The meaningful 4-letter words that can be formed are "each" and "ache". So, the total number is two.

Q3. Nine players take part in a round-robin tournament where every player faces each of the others exactly once. What is the total number of matches?

1. 72
2. 40
3. 42
4. 36

Answer: 36

In a round-robin tournament, each match is played between a pair of players. The total number of matches is ${}^9C_2 = \frac{9\times 8}{2} = 36$.