Question

Find the value of 7C3

Answer 1

Answer:

35

Step-by-step explanation:

Answer 2

SOLUTION

TO DETERMINE

$\displaystyle \sf{ {}^{7} C_3 }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

$\displaystyle \sf{ {}^{n} C_r= \frac{n!}{r!(n- r)!} }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ {}^{7} C_3 }$

We simplify it as below

$\displaystyle \sf{ {}^{7} C_3 }$

$\displaystyle \sf{ = \frac{7!}{3!(7 - 3)!} }$

$\displaystyle \sf{ = \frac{7!}{3! \: 4!} }$

$\displaystyle \sf{ = \frac{7 \times 6 \times 5 \times 4!}{3! \times \: 4!} }$

$\displaystyle \sf{ = \frac{7 \times 6 \times 5 }{3! } }$

$\displaystyle \sf{ = \frac{7 \times 6 \times 5 }{3 \times 2 } }$

$\displaystyle \sf{ = \frac{7 \times 6 \times 5 }{6} }$

$\displaystyle \sf{ = 7 \times 5}$

$\displaystyle \bf{ = 35 }$

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