Answer to Question #284727 in Combinatorics | Number Theory for kool

Question

In a Zoo, there are 6 Bengal white tigers and 7 Bengal royal tigers. Out of these tigers, 5 are males and 10 are either Bengal royal tigers or males. Find the number of female Bengal white tigers in the Zoo.

Answer 1

Solution:

Denotation-

Bengal white tigers = W

Bengal royal tigers = R

Males = M and

Females = F.

Given, $n(W)=6, n(R)=7, n(M)=5, n(F)=8, n(R\cup M)=10$

$\Rightarrow n(T)=n(W)+n(R)=6+7=13.$

Also, $n(R\cap M)=n(R)+n(M)-n(R\cup M)$

$\Rightarrow n(R\cap M)=7+5-10=2$

Now, $n(W\cap F)=n(W)+n(F)-n(W\cup F)$ ...(i)

Consider $n(W\cup F)$

$=n(T)-n(R\cap M) \\=13-2 \\=11$

Putting this value in (i).

$n(W\cap F)=6+8-11=3$

Thus, the number of female Bengal white tigers in the Zoo is 3.