The board of directors of a pharmaceutical corporation has 10 members. Three members of the board of directors are physicians. How many different slates consisting of a president, vice president, secretary, and treasurer be made with exactly one physician. Note that there are 3 physicians out of the 10 directors.

PoentWeptgj 2022-07-15 Answered
The board of directors of a pharmaceutical corporation has 10 members. Three members of the board of directors are physicians. How many different slates consisting of a president, vice president, secretary, and treasurer be made with exactly one physician. Note that there are 3 physicians out of the 10 directors.
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Answers (1)

taguetzbo
Answered 2022-07-16 Author has 16 answers
Step 1
You must consider also all the ways to arrange the people into the positions.
Step 2
You have 4 distinct positions to fill, choose 1 of 3 physicians, and 3 of 7 other members (non-physician) to fill the positions.
4 ! × 3 C 1 × 7 C 3 = 4 × 3 × ( 7 × 6 × 5 )

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