Question

In how many ways can a student choose 6 courses out of 10 courses?

• A. $5040$
• B. $210$
• C. $6!$
• D. $\frac{6!}{3!}$

Answer 1

The correct option is B $210$

We know that number of ways of selecting "r" things out of "n" things at a time is equal to ${}^n{C}_r=\frac{n!}{(n-r)!\times r!}.$

According to question student have to select $6$ courses out of $10$ courses.

Number of ways of doing that is ${}^{10}{C}_6=\frac{10!}{(10-6)!\times 6!}=\frac{10!}{4!\times 6!}$

$\Rightarrow {}^{10}{C}_6=\frac{10\times 9\times 8\times 7\times 6!}{24\times 6!}=\frac{5040}{24}=210$