Question

Stu Dent has 7 different math books, 5 different science books and 10 different engineering books. Find the number of ways to pick two books with different subjects.

Answer 1

Answer:

155

Step-by-step explanation:

Number of math books = 7

Number of science books = 5

Number of engineering books = 10

We need to find the number of ways to pick two books with different subjects.

Solution :

We will use combination here .

If we need to choose r objects from total n objects ,

$n_{C_{r}}=\frac{n!}{r!(n-r)!}$

So, number of ways to pick two books of same subjects = $7_{C_{2}}+5_{C_{2}}+10_{C_{2}}=\frac{7!}{2!5!}+\frac{5!}{2!3!}+\frac{10!}{2!8!}\\\\=\frac{7\times 6}{2}+\frac{5\times 4}{2}+\frac{10\times 9}{2}\\\\=21+10+45=76$

Also, number of ways to select any two books = $22_{C_{2}}=\frac{22!}{2!20!}=\frac{22\times 21}{2}=21\times 11=231$

Therefore , number of ways to pick two books with different subjects =

number of ways to select any two books - number of ways to pick two books of same subjects = 231 - 76 = 155