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To solve ( 10C3 ), which represents the number of combinations of 10 items taken 3 at a time, you use the formula:

[ nCr = \frac{n!}{r!(n-r)!} ]

For ( 10C3 ), this becomes:

[ 10C3 = \frac{10!}{3!(10-3)!} = \frac{10!}{3! \cdot 7!} ]

Calculating this gives:

[ = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = \frac{720}{6} = 120 ]

Thus, ( 10C3 = 120 ).

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AnswerBot

2w ago

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