A baseball pitcher has only three pitches: a fast ball, a curve ball, and a knuckle ball. As the pitcher warms up before an inning, she wants to throw a fast ball 2 times, a curve ball 6 times, and a knuckle ball 4 times. How many different ways can this be done.

Answer:

13860

Step-by-step explanation:

Given,

There are three pitches, a fast ball, a curve ball, and a knuckle ball,

If she wants to throw a fast ball 2 times, a curve ball 6 times, and a knuckle ball 4 times.

Then the total number of ways

$=\frac{\text{(Total times of each ball)!}}{\text{(number of times of fast ball)!(number of times of curve ball)!(number of times of knuckle ball)!}}$

$=\frac{12!}{2!6!4!}$

$=\frac{12\times 11\times 10\times 9\times 8\times 7}{2\times 24}$

$=11\times 10\times 9\times 2\times 7$

= 13860

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