40320 batting orders are possible.
Since the pitcher bats last, there is only one choice for the 9th slot. For the 1st slot, there are 8 choices remaining. For the 2nd slot, there are 7 choices remaining, etc.
So the number of possible batting orders is:
8*7*6*5*4*3*2*1 = 8! = 40,320
factorial, in mathematics, the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point. Thus, factorial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is defined as equal to 1.
Factorials are commonly encountered in the evaluation of permutations and combinations and in the coefficients of terms of binomial expansions .
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Since the pitcher bats last, there is only one choice for the 9th slot. For the 1st slot, there are 8 choices remaining. For the 2nd slot, there are 7 choices remaining, etc.
So the number of possible batting orders is:
8*7*6*5*4*3*2*1 = 8! = 40,320
factorial, in mathematics, the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point. Thus, factorial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is defined as equal to 1.
Factorials are commonly encountered in the evaluation of permutations and combinations and in the coefficients of terms of binomial expansions .
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