Question

minta tolong dikerjakan dengan caranya ya kak

Answer 1

Kombinasi

..

[tex]\boxed{_nC_r = \frac{n!}{(n - r)!r!} }[/tex]

soal a.

[tex]\begin{aligned} _5C_4 &= \frac{5!}{(5-4)!4!} \\&= \frac{5 × 4!}{4!} \\&= \frac{5 × \cancel{4!}}{\cancel{4!}} \\&= \boxed{ 5} \end{aligned}[/tex]

soal b.

[tex]\begin{aligned} _7C_5 &= \frac{7!}{(7 - 5)!5!} \\&= \frac{7 × 6 × 5!}{2!×5!} \\&= \frac{7 × 6 × \cancel{5!}}{2×\cancel{5!}} \\&= \frac{42}{2} \\&= \boxed{ 21 }\end{aligned}[/tex]

soal c.

[tex]\begin{aligned} \frac{_5C_3._7C_2}{_{12}C_5} &= \frac{ \frac{5!}{(5 - 3)!3!} \times \frac{7!}{(7 - 2)!2!} }{ \frac{12!}{(12 - 5)!5!} } \\&= \frac{ \frac{5 \times 4 \times 3!}{2!3!} \times \frac{7 \times 6 \times 5!}{5!2!} }{ \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{7!5!} } \\&= \frac{ \frac{5 \times 4 }{2} \times \frac{7 \times 6 }{2} }{ \frac{12 \times 11 \times 10 \times 9 \times 8 }{5!} } \\&= \frac{ \frac{20 }{2} \times \frac{42 }{2} }{ \frac{95040 }{120} } \\&= \frac{10 \times 21}{792} \\&= \frac{5 \times 7}{132} \\&= \boxed{ \frac{35}{132} } \end{aligned}[/tex]

[tex]\begin{array}{lr}\texttt{Selamat Menunaikan Ibadah Puasa}\end{array}[/tex]

[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at | 03 - 04 - 2023}}[/tex]