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

Question #284727

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.


1
Expert's answer
2022-01-05T03:46:41-0500

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

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

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

n(RM)=7+510=2\Rightarrow n(R\cap M)=7+5-10=2

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

Consider n(WF)n(W\cup F)

=n(T)n(RM)=132=11=n(T)-n(R\cap M) \\=13-2 \\=11

Putting this value in (i).

n(WF)=6+811=3n(W\cap F)=6+8-11=3

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


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