Browse · MATH

jmc

counting and probability junior

Problem

Compute

(4 13) + (9 13)

.

Solution

Note that

(4 13) = \frac{13 !}{4 ! 9 !} = (9 13)

. Thus, we have

(4 13) + (9 13) = 2 \times (4 13) = 2 \times \frac{13 !}{4 ! 9 !} = 2 \times \frac{13 \times 12 \times 11 \times 10}{4 \times 3 \times 2 \times 1} = 2 \times 13 \times \frac{12}{4 \times 3} \times 11 \times \frac{10}{2 \times 1} = 2 \times 13 \times 1 \times 11 \times 5 = 13 \times 11 \times 10 = 1430 .

Final answer

1430