Answer:
n[total]=25
n[top finishers]=8
the number of possible outcome
=[tex] \frac{25 \times 24 \times 23 \times 22 \times 21 \times 20 \times 19 \times 18}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} = 1081575[/tex]outcomes
Answer:
[tex] \large\boxed{ \boxed{\rm 1081575 \: outcomes}}[/tex]
Step-by-step explanation:
to determine the number of possible outcomes we can consider Combination given by
[tex] \displaystyle \binom{n}{r} = \frac{n!}{r!(n - r)!} [/tex]
where:
so let n and r be 25 and 8 respectively thus
substitute:
[tex] \displaystyle \binom{25}{8} = \frac{25!}{8!(25- 8)!} [/tex]
simplify parentheses:
[tex] \displaystyle \binom{25}{8} = \frac{25!}{8! \times 17!} [/tex]
rewrite numeratorr:
[tex] \rm \displaystyle \binom{25}{8} = \frac{25 \times 24 \times 23 \times 22 \times 21 \times 20 \times 19 \times 18 \times 17!}{8! \times 17!} [/tex]
reduce fraction:
[tex]\rm \displaystyle \binom{25}{8} = \frac{25 \times 24 \times 23 \times 22 \times 21 \times 20 \times 19 \times 18 }{8! } [/tex]
simplify numerator and denominator:
[tex]\rm \displaystyle \binom{25}{8} = \frac{43609104000}{40320 } [/tex]
simplify division:
[tex]\rm \displaystyle \binom{25}{8} = 1081575[/tex]
hence,
the number of outcomes is 1081575
