a. Evaluate 7C3 using factorials. b. What is the difference between a permutation and a

Chapter 9, Problem R.5

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QUESTION:

a. Evaluate \({ }_{7} C_{3}\) using factorials.

b. What is the difference between a permutation and a combination?

c. The 12th-grade class at Scorpion Gulch High School has 100 students: 53 girls and 47 boys. In how many different ways could they select the following?

i. A group of four students to be class officers

ii. A president, a vice president, a secretary, and a treasurer

iii. A seven-member debate team consisting of four boys and three girls

d. If a seven-member debate team is selected at random as in part c, what is the probability that it will have four boys and three girls?

Questions & Answers

QUESTION:

a. Evaluate \({ }_{7} C_{3}\) using factorials.

b. What is the difference between a permutation and a combination?

c. The 12th-grade class at Scorpion Gulch High School has 100 students: 53 girls and 47 boys. In how many different ways could they select the following?

i. A group of four students to be class officers

ii. A president, a vice president, a secretary, and a treasurer

iii. A seven-member debate team consisting of four boys and three girls

d. If a seven-member debate team is selected at random as in part c, what is the probability that it will have four boys and three girls?

ANSWER:

Step 1 of 4

a) Evaluating  using factorials:

 

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