Q1. A supervisor is evaluating ten subordinates for their annual performance reviews. According to a new corporate policy, for every ten employees, two must be evaluated as “exceeds expectations,” seven as “meets expectations,” and one as “does not meet expectations.” How many different ways is it possible for the supervisor to assign these ratings?

A)   10,080.

B)   5,040.

C)   360.

Q2. A firm wants to select a team of five from a group of ten employees. How many ways can the firm compose the team of five?

A)   120.

B)   252.

C)   25.

Q3. A portfolio manager wants to eliminate four stocks from a portfolio that consists of six stocks. How many ways can the four stocks be sold when the order of the sales is important?

A)   180.

B)   24.

C)   360.

答案和详解如下：

Q1. A supervisor is evaluating ten subordinates for their annual performance reviews. According to a new corporate policy, for every ten employees, two must be evaluated as “exceeds expectations,” seven as “meets expectations,” and one as “does not meet expectations.” How many different ways is it possible for the supervisor to assign these ratings?

A)   10,080.

B)   5,040.

C)   360.

Correct answer is C)       

The number of different ways to assign these labels is:

Q2. A firm wants to select a team of five from a group of ten employees. How many ways can the firm compose the team of five?

A)   120.

B)   252.

C)   25.

Correct answer is B)

This is a labeling problem where there are only two labels: chosen and not chosen. Thus, the combination formula applies: 10! / (5! × 5!) = 3,628,800 / (120 × 120) = 252.

With a TI calculator: 10 [2nd][nCr] 5 = 252.

Q3. A portfolio manager wants to eliminate four stocks from a portfolio that consists of six stocks. How many ways can the four stocks be sold when the order of the sales is important?

A)   180.

B)   24.

C)   360.

Correct answer is C)

This is a choose four from six problem where order is important. Thus, it requires the permutation formula: n! / (n − r)! = 6! / (6 − 4)! = 360.

With TI calculator: 6 [2nd][nPr] 4 = 360.

Thanks

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