Permutation and Combination

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

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

Answer

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

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

• (a) 220
• (b) 495
• (c) 2145
• (d) 792

Answer

Correct Answer: (c) 2145
The number of ways to choose 4 balls from the box containing 5 red balls, 4 green balls, and 3 blue balls is ^{12}C_{4} = \frac{12!}{4!(12-4)!} = 2145 .

(48) How many different 5-letter words can be formed using the letters of the word “SUNDAY”?

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

Answer

Correct Answer: (c) 1440
The number of different 5-letter words that can be formed using the letters of the word “SUNDAY” is \frac{6!}{2!} = 1440 .

(49) 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 .

(50) How many different ways can you choose 5 marbles from a bag containing 12 red marbles and 8 blue marbles?

• (a) 792
• (b) 120
• (c) 792
• (d) 1260

Answer

Correct Answer: (c) 792
The number of ways to choose 5 marbles from the bag containing 12 red marbles and 8 blue marbles is ^{20}C_{5} = \frac{20!}{5!(20-5)!} = 792 .