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Katyanochek1 [597]
4 years ago
10

HELP!!!! WILL GIVE BRAINLIEST TO FIRST RIGHT ANSWER!!!

Mathematics
1 answer:
bixtya [17]4 years ago
4 0

Answer:

\large \boxed{\text{1. 24024; 2. 2002}}

Step-by-step explanation:

1. Appointment of officers

The officers have a hierarchy, so order is important.

We must choose the number of permutations.

\begin{array}{rcl}_{14}P_{4} & = & \dfrac{14!}{(14 - 4)!}\\\\ & = & \dfrac{14!}{10!}\\\\  & = & 14 \times 13 \times 12 \times 11\\ & = & \mathbf{24024}\\\end{array}\\\text{You can choose the officers in $\large \boxed{\mathbf{24024}}$ ways.}

2. Appointment of committee

Any five of the 14 members can be appointed to the Planning Committee.

The order of appointment doesn't matter, so we must choose the number of combinations.

\begin{array}{rcl}_{14}C_{5} & = & \dfrac{14!}{5!(14 - 5)!}\\\\ & = & \dfrac{14!}{5!9!}\\\\  & = & \dfrac{14 \times 13 \times 12 \times 11 \times 10}{120}\\\\ & = & \mathbf{2002}\\\end{array}\\\text{You can choose the committee in $\large \boxed{\mathbf{2002}}$ ways.}

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2 years ago
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3 years ago
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