Question

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

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

Answer 1

Answer: (B)

Number of ways in which the tourist can visit the zebras (he can visit with no zebra or $1$ zebra or ... $20^{th}$ zebra)
$= \,{}^{20}C_0 + \,{}^{20}C_1 + ... + \,{}^{20}C_{20} = 2^{20}$
Similarly, the ways to visit $12$ giraffes $= 2^{12}$
Ways to visit $11$ lions $= 2^{11}$
Now, restrictions on tigers : Number of ways
$= (^3C_0 + \,{}^3C_1 + \,{}^3C_2 + \,{}^3C_3 - \,{}^3C_0)$
$= 2^3 - 1 = 7$
$\therefore $ Required number of ways $= 2^{20} \times 2^{12} \times 2^{11} \times 7$
$= 7 \cdot 2^{43}$