Question

A zoo has $20$ zebras, $12$ giraffes, $11$ lions and $3$ tigers. The number of ways a tourist can visit the zoo, so that he must see at least one tiger is

• A. $21\times 13\times 12\times 3$
• B. $7\times 2^{43}$
• C. $7\times 21\times 13\times 12-1$
• D. $6\times 2^{43}$

Answer 1

The correct option is B $7\times 2^{43}$

There are total $20$ zebras.

Each zebra is either seen OR not seen by the tourist, that is $2$ ways of doing the task.
So, for $20$ zebras the tourist can either see or not see all in $2^{20}$ ways. ($2\times 2\times 2\times \mathrm{2........20}times$).
Similarly, number of ways of watching the $12$ jiraffes is equal to $2^{12}$.
Number of ways of watching $11$ lions is $2^{11}$.
Number of ways of watching $3$ tigers is $2^3$, which will include one case when the tourist watches neither of them. Since, he must watch at least one tiger, excluding this one case, we get the number of ways of watching tigers is $2^3-1$.
Hence, the total number of ways of visiting the zoo, so that the tourist watches at least one tiger, using multiplication principle, is equal to
$2^{20}\times 2^{12}\times 2^{11}\times (2^3-1)$
$=2^{43}\times 7$