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  • Maha asks her son to select five pencils from the box. How many different answers could the son provide if there were 10 pencils in the box to choose from?<str

Maha asks her son to select five pencils from the box. How many different answers could the son provide if there were 10 pencils in the box to choose from?

Option: 1

168 


Option: 2

252


Option: 3

284 

 


Option: 4

332


Answers (1)

best_answer

Given that,
r = 5\\

n = 10

The number of combinations is given by,

\begin{aligned} &C(n, r)=\frac{n !}{r !(n-r) !}\\ &C(10,5)=\frac{10 !}{5 !(10-5) !}\\ &C(10,5)=\frac{10 !}{5 ! 5 !} \end{aligned}

\begin{aligned} & C(10,5)=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2}{5 \times 4 \times 3 \times 2 \times 5 \times 4 \times 3 \times 2} \\ & C(10,5)=252 \end{aligned}

Therefore, the total number of possible answers is 252.

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manish

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