Question

98. XYZ Corporation hired 6 people as

summer workers. Of these 6 people, 3 will

be hired as permanent employees in the

fall. If 2 of the 6 people are male, how

many of the possible groups of 3 people

hired in the fall will include only 1 male?

E. 4

F. 6

G. 12

H. 24

Answer 1

G. 12

Explanation:

You want the number of ways 1 male and 2 females can be chosen from a group of 2 males and 4 females.

Males

From a group of 2 males, there are 2 ways that 1 male can be chosen. (He can be one, or the other.

Females

From a group of 4 females, there can be 4C2 = 4!/(2!(2!)) = 4·3/2 = 6 ways that 2 females can be chosen.

Possible groups

The total number of possible groups is the product of the numbers of groups of males and of females:

possible groups = 2 · 6 = 12

G. There are 12 possible groups of 3 people.

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Additional comment

If the males are {a, b} and the females are {A, B, C, D}, the 12 possible groups are ...

aAB aAC aAD aBC aBD aCD bAB bAC bAD bBC bBD bCD

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