align* 102 83 &= 10!2!8! 8!3!5! &= 10!2!3!5! &= 10 9 8 7 6(2 1) (3 2 1) &= 102 1 9 8 7 63 2 1 &= 5 9 8 7 1 &= 2520. align*

Browse · MATH

jmc

counting and probability junior

Problem

Compute

(2 10) \times (3 8)

Solution

(2 10) \times (3 8) = \frac{10 !}{2 ! 8 !} \times \frac{8 !}{3 ! 5 !} = \frac{10 !}{2 ! 3 ! 5 !} = \frac{10 \times 9 \times 8 \times 7 \times 6}{( 2 \times 1 ) \times ( 3 \times 2 \times 1 )} = \frac{10}{2 \times 1} \times 9 \times 8 \times 7 \times \frac{6}{3 \times 2 \times 1} = 5 \times 9 \times 8 \times 7 \times 1 = 2520 .

Final answer

2520