Question

How do you find the value of the combination \[C\left( {6,6} \right)\] ?

Answer 1

Hint: Given is the combination. We are given with the values of both n and r. We will directly use the formula to find the answer. Permutation is used to find the number of arrangements and selections in different cases.
Formula used:
 \[{}^n{C_r} = \dfrac{{n!}}{{r!\left( {n - r} \right)!}}\]

Complete step by step solution:
Given that \[C\left( {6,6} \right)\] .
Comparing it with \[C\left( {n,r} \right)\] we get \[n = 6,r = 6\]
Putting the values in the formula,
 \[{}^6{C_6} = \dfrac{{6!}}{{6!\left( {6 - 6} \right)!}}\]
On calculating the brackets,
 \[{}^6{C_6} = \dfrac{{6!}}{{6!\left( 0 \right)!}}\]
We know that \[0! = 1\] putting this in the above formula,
 \[{}^6{C_6} = \dfrac{{6!}}{{6!}}\]
Cancelling the factorial,
 \[{}^6{C_6} = 1\]
This is our answer.
So, the correct answer is “1”.

Note: Here note that we have to find the combination. We are given with the values of n and r. so use them wisely. If misarranged then the answer will be wrong. Also note that though the values of n and r are the same the answer for 0! Is not zero rather it is one.
Combination is selection that can be formed by taking some or all sets of things.
Combination can be expressed as \[{}^n{C_r}\] or \[C\left( {n,r} \right)\] .