5 People can be chosen in 1287 ways if the order in which they are chosen is not important.
Step-by-step explanation:
Given:
Total number of students= 13
Number of Students to be selected= 5
To Find :
The number of ways in which the 5 people can be selected=?
Solution:
Let us use the permutation and combination to solve this problem
[tex]nCr=\frac{(n)!}{(n-r)!(r)!}[/tex]
So here , n =13 and r=5 ,
So after putting the value of n and r , the equation will be
[tex]13C_5=\frac{(13)!}{(13-5)!(5)!}[/tex]
[tex]13C_5=\frac{(13 \times12 \times11 \times10 \times9 \times8\times7 \times6 \times5 \times4 \times3 \times2 \times1)}{(8 \times7 \times6 \times5 \times4 \times3 \times2 \times1)(5 \times4 \times3 \times2 \times1)}[/tex]
[tex]13C_5=\frac{(13 \times12 \times11 \times10 \times9 )}{((5 \times4 \times3 \times2 \times1)}[/tex]
[tex]13C_5=\frac{154440}{120}[/tex]
[tex]13C_5= 1287[/tex]
