Question

If nc3=20, then find the value of n

Answer 1

Answer:

REFER TO THE ATTACHMENT

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Answer 2

The value of n = 6

Given :

$\displaystyle \sf{ {}^{n}C_3 = 20 }$

To find :

The value of n

Formula :

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

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

$\displaystyle \sf{ {}^{n}C_3 = 20 }$

Step 2 of 2 :

Find the value of n

$\displaystyle \sf{ {}^{n}C_3 = 20 }$

$\displaystyle \sf{ \implies {}^{n}C_3 = \frac{6 \times 5 \times 4}{6} }$

$\displaystyle \sf{ \implies {}^{n}C_3 = \frac{6!}{3!3!} }$

$\displaystyle \sf{ \implies {}^{n}C_3 = \frac{6!}{3!(6 - 3)!} }$

$\displaystyle \sf{ \implies {}^{n}C_3 = {}^{6}C_3 } \: \: \bigg[ \: \because \:\displaystyle \sf{ {}^{n}C_r = \frac{n!}{r!(n - r)!} } \: \bigg]$

$\displaystyle \sf{ \implies n = 6}$

Hence the required value of n = 6

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