Question

Someone help I think this is probability but I don’t know

Answer 1

ANSWER

1. 3391680

2. 3876

EXPLANATION

1. We want to find the value of:

$P^{12}_7$

This is called "12 permutation 7"

Permutation function is defined as follows:

$P^n_r\text{ = }\frac{n!}{(n-r)!}$

Therefore, we have that:

$\begin{gathered} P^{12}_7=\frac{12!}{(12\text{ - 7)}!}\text{ = }\frac{12!}{5!} \\ P^{12}_7=\frac{12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!} \\ P^{12}_7=\text{ 12 }\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6 \\ P^{12}_7=3391680 \end{gathered}$

2. We want to find:

$C^{19}_{15}$

This is called "19 combination 15"

Combination function is defined as:

$C^n_r=\frac{n!}{(n-r)!\cdot r!_{}}$

Therefore, we have that:

$\begin{gathered} C^{19}_{15}\text{ = }\frac{19!}{(19-15)!\cdot15!}\text{ = }\frac{19!}{4!\cdot15!} \\ ^{}C^{19}_{15}=\frac{19\cdot18\cdot17\cdot16\cdot15!}{4\cdot3\cdot2\cdot1\cdot15!} \\ C^{19}_{15}=\frac{19\cdot18\cdot17\cdot16}{4\cdot3\cdot2\cdot1} \\ C^{19}_{15}=\text{ 3876} \end{gathered}$