Permutation and Combination

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

• (a) 725760
• (b) 181440
• (c) 72576
• (d) 14400

Answer

Correct Answer: (c) 72576
The number of different ways to arrange the letters of the word “ALGORITHM” is \frac{9!}{2!2!} = 72576 .

(37) A box contains 6 red balls, 5 green balls, and 4 blue balls. In how many ways can you choose 4 balls from the box?

• (a) 330
• (b) 495
• (c) 1001
• (d) 1260

Answer

Correct Answer: (c) 1001
The number of ways to choose 4 balls from the box containing 6 red balls, 5 green balls, and 4 blue balls is ^{15}C_{4} = \frac{15!}{4!(15-4)!} = 1001 .

(38) How many different 7-letter words can be formed using the letters of the word “SYNTAXES”?

• (a) 1440
• (b) 2520
• (c) 5040
• (d) 1260

Answer

Correct Answer: (c) 5040
The number of different 7-letter words that can be formed using the letters of the word “SYNTAXES” is \frac{7!}{2!} = 5040 .

(39) 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) 120

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 .

(40) How many different ways can you choose 5 marbles from a bag containing 9 red marbles and 7 blue marbles?

• (a) 792
• (b) 1260
• (c) 126
• (d) 252

Answer

Correct Answer: (c) 126
The number of ways to choose 5 marbles from the bag containing 9 red marbles and 7 blue marbles is ^{16}C_{5} = \frac{16!}{5!(16-5)!} = 126 .