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How do you evaluate 10c3?

Answer 1

Jonathan Allen

#10C3 = 120#

#color(white)("x")_(10)C_3#

#color(white)("XXXX")=(10!)/((10-3)! * (3!))#

#color(white)("XXXX")=(10 xx 9 xx 8 xx cancel(7 xx 6 xx ... xx1))/(cancel(7 xx 6 xx ... xx 1) * (3 xx 2 xx1))#

#color(white)("XXXX")=(10 xx cancel(9)^3 xx cancel(8)^4)/(cancel(3) xx cancel(2) xx1)#

#color(white)("XXXX")=120#

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Answer 2

Hailey Anderson

To evaluate ( \binom{10}{3} ), also known as "10 choose 3," you use the combination formula, which is:

[ \binom{n}{k} = \frac{n!}{k!(n-k)!} ]

Substitute ( n = 10 ) and ( k = 3 ) into the formula:

[ \binom{10}{3} = \frac{10!}{3!(10-3)!} ]

Simplify the factorials:

[ \binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} ]

[ \binom{10}{3} = \frac{720}{6} ]

[ \binom{10}{3} = 120 ]

So, ( \binom{10}{3} ) equals 120.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.