Question

kk bantuin plis soalnya mau dikumpulkan ​

Answer 1

Penjelasan dengan langkah-langkah:

Kombinasi

1.a

[tex]\begin{aligned}_{7}C_{2}&=\frac{7!}{2!(7-2)!}\\&=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(2 \times 1)(5 \times 4 \times 3 \times 2 \times 1)} \\& = \frac{7 \times 6}{2 \times 1} \\& = 21 \end{aligned}[/tex]

1.b

[tex]\begin{aligned}_{8}C_{3}&=\frac{8!}{3!(8-3)!}\\&=\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(3 \times 2 \times 1)(5 \times 4 \times 3 \times 2 \times 1)} \\& = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} \\& = 56 \end{aligned}[/tex]

1.c

[tex]\begin{aligned}_{10}C_{9}&=\frac{10!}{9!(10-9)!}\\&=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)( 1)} \\& = \frac{10}{1} \\& = 10 \end{aligned}[/tex]

2.

[tex]\begin{aligned}_{n}C_{2}&=7n \\ \frac{n!}{2!(n - 2)!} & = 7n \\ \frac{n!}{2!(n - 2)!} - 7n& = 0 \\ \frac{n! - 7 \times 2! \times n(n - 2)!}{2!(n - 2)!} & = 0 \\ n! - 7 \times 2!n(n - 2)! &= 0 \\ (n(n - 1) - 7 \times 2n)(n - 2)! & = 0 \\ ( {n}^{2} - n - 14n )(n - 2)!& = 0 \\ ( {n}^{2} - 15n )(n - 2)!& = 0\end{aligned}[/tex]

Diperoleh

[tex]\rm n_1 \Rightarrow n^2 -15n=0\\n(n-15)=0\\n=0\:dan\:\:n=15[/tex]

[tex]\rm n_2 \Rightarrow (n-2)!=0\\n=∅[/tex]

Untuk

n = 0

n = 15

karena 0 tidak memenuhi , maka nilai n adalah 15 ✓