Question

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

Answer 1

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.

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