Respuesta :
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 ,
[tex]n_{C_{r}}=\frac{n!}{r!(n-r)!}[/tex]
So, number of ways to pick two books of same subjects = [tex]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[/tex]
Also, number of ways to select any two books = [tex]22_{C_{2}}=\frac{22!}{2!20!}=\frac{22\times 21}{2}=21\times 11=231[/tex]
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
