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help please and explain your answer please !!!!!!!!!!! Houston Elementary School is selecting students to be in the winter festival show. There are 4 roles left but there are 12 students interested in the roles. How many combinations of the twelve students can be chosen for the four remaining roles? A. 505 B.495 C.48 D.16

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musiclover10045
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Answer: 495

Step-by-step explanation:

nCr = n!/(n-r)!r!

12C4 = 12!/(12-4)!4!

=12!/8!4!

= 12 ×11×10×9×8! / 8!4!

8! at the numerator will cancel that of denominator

= 12×11×10×9 / 4!

=11880/4×3×2

=11880/24

=495

Therefore; 12C4 = 495

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