Question

Chris is practicing basketball How many ways can he make exactly 3 baskets in 6 tries?

Answer 1

• n=6
• r=3
• Here a word exactly given so we apply combination

$\\ \sf\longmapsto {}^nC_r=\dfrac{n!}{r!(n-r)!}$

$\\ \sf\longmapsto {}^6C_3$

$\\ \sf\longmapsto \dfrac{6!}{3!(6-3)!}$

$\\ \sf\longmapsto \dfrac{6\times 5\times 4\times 3!}{3!3!}$

$\\ \sf\longmapsto \dfrac{120}{3!}$

$\\ \sf\longmapsto \dfrac{120}{6}$

$\\ \sf\longmapsto 30$

Answer 2

☄Answer : -

nCr = n! ÷ (n - r)!r!

6C3 = 6! ÷ (6 - 3)!3!

6C3 = 6! ÷ 3!3!

6C3 = 6•5•4•3! ÷ 3!3!

6C3 = 6•5•4 ÷ 3!

6C3 = 5•4

6C3 = 20✔