Question

6C2 how will we solve this

Answer 1

Hi ...dear...here is your answer. .
. .......see picture for full explanation.. !!!
..... hope you understand!!!
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#shubhendu

Answer 2

$6 c_{2} = 15$

Solution:

Given that we have to solve:

$6c_2$

This is a combination sum

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

The formula for combination is given as:

$\mathrm{nc}_{\mathrm{r}}=\frac{\mathrm{n!}}{(\mathrm{n}-\mathrm{r}) ! \mathrm{r!}}$

where n represents the total number of items, and r represents the number of items being chosen at a time.

Here we have to chose 2 items from 6

So n = 6 and r = 2

$6 c_{2}=\frac{6 !}{(6-2) ! 2 !}$

Factorial of a number n is the product of all positive numbers less than equal to n.

For example, for the number 3 the factorial of 3 will be $3 \times 2 \times 1$

So we get,

$\begin{aligned}&6 c_{2}=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 ! 2 !}\\\\&6 c_{2}=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1 \times 2 \times 1}\end{aligned}$

On solving,

$6 c_{2}=3 \times 5=15$

Thus $6 c_{2} = 15$

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