Question

Seven different prizes are to be distributed among three contest winners such that each winner receives at least one prize and each of the prizes goes to one of the three winners. In how many different ways can the prizes be distributed among the three winners

Answer 1

Answer:

The answer is "35"

Step-by-step explanation:

$\to n=7\\\\\to r=3\\\\Formula:\\\\\to {}^{n}C_{r}= \binom{n}{r}= \frac{n!}{r!(n-r)!}$

$\to {}^{7}C_{3}= \binom{7}{3}= \frac{7!}{3!(7-3)!}$

                    $= \frac{7\times 6 \times 5 \times 4!}{3! \times 4!}\\\\= \frac{7\times 6 \times 5 }{3!}\\\\= \frac{7\times 6 \times 5 }{3\times 2 \times 1}\\\\ = 7 \times 5 \\\\= 35$