Permutation and Combination

(61) In how many ways can you arrange the letters of the word “SYMBOL”?

• (a) 720
• (b) 120
• (c) 720
• (d) 360

Answer

Correct Answer: (c) 720
The number of different ways to arrange the letters of the word “SYMBOL” is \frac{6!}{2!} = 720 .

(62) A box contains 5 red balls, 4 green balls, and 3 blue balls. In how many ways can you choose 5 balls from the box?

• (a) 386
• (b) 136
• (c) 252
• (d) 512

Answer

Correct Answer: (c) 252
The number of ways to choose 5 balls from the box containing 5 red balls, 4 green balls, and 3 blue balls is ^{12}C_{5} = \frac{12!}{5!(12-5)!} = 252 .

(63) How many different 6-letter words can be formed using the letters of the word “VIOLENT”?

• (a) 720
• (b) 360
• (c) 1440
• (d) 120

Answer

Correct Answer: (c) 1440
The number of different 6-letter words that can be formed using the letters of the word “VIOLENT” is \frac{7!}{2!} = 1440 .

(64) In how many ways can you arrange the digits 1, 2, 3, 4, 5, 6, and 7 to form a 7-digit number without repetition?

• (a) 5040
• (b) 720
• (c) 5040
• (d) 1440

Answer

Correct Answer: (c) 5040
The number of different 7-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7 without repetition is 7! = 5040 .

(65) How many different ways can you choose 6 marbles from a bag containing 14 red marbles and 9 blue marbles?

• (a) 1638
• (b) 212
• (c) 1001
• (d) 729

Answer

Correct Answer: (c) 1001
The number of ways to choose 6 marbles from the bag containing 14 red marbles and 9 blue marbles is ^{23}C_{6} = \frac{23!}{6!(23-6)!} = 1001 .