Permutation and Combination

(1) From a group of 8 people, how many ways can we choose a committee of 4?

• (a) 56
• (b) 70
• (c) 56
• (d) 28

Answer

Correct Answer: (b) 70
The number of ways to choose a committee of 4 from 8 people is given by ^8C_4 = \frac{8!}{4!(8-4)!} which equals 70.

(2) How many ways can 5 out of 10 books be arranged on a shelf?

• (a) 6048
• (b) 30240
• (c) 25200
• (d) 181440

Answer

Correct Answer: (b) 30240
The number of ways to arrange 5 books out of 10 on a shelf is given by 5! \times ^{10}C_{5} = 5! \times \frac{10!}{5!(10-5)!} which equals 30240.

(3) In how many ways can a president, vice president, and treasurer be chosen from a group of 12 candidates?

• (a) 440
• (b) 1320
• (c) 5280
• (d) 220

Answer

Correct Answer: (b) 1320
The number of ways to choose a president, vice president, and treasurer from 12 candidates is given by 3! \times ^{12}C_{3} = 3! \times \frac{12!}{3!(12-3)!} which equals 1320.

(4) How many ways can you arrange the letters of the word “APPLE”?

• (a) 120
• (b) 60
• (c) 24
• (d) 720

Answer

Correct Answer: (a) 120
The number of ways to arrange the letters of the word “APPLE” is given by 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 .

(5) In how many ways can you choose 3 different books out of a collection of 10 different books to read during a trip?

• (a) 120
• (b) 45
• (c) 210
• (d) 720

Answer

Correct Answer: (a) 120
The number of ways to choose 3 different books out of 10 different books is given by ^{10}C_{3} = \frac{10!}{3!(10-3)!} = 120 .