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

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 × 13 × 12 × 3 (B) 7 ⋅ 243 (C) 7 × 21 × 13 × 12 (D) 6 ⋅ 243

Tardigrade Admin · Accepted Answer

Number of ways in which the tourist can visit the zebras (he can visit with no zebra or

1

zebra or ...

2 0^{t h}

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

= (^{3} C_{0} +^{3} C_{1} +^{3} C_{2} +^{3} C_{3} -^{3} C_{0})

= 2^{3} - 1 = 7

∴

Required number of ways

= 2^{20} \times 2^{12} \times 2^{11} \times 7

= 7 \cdot 2^{43}

Q. 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

$21 \times 13 \times 12 \times 3$

$7 \cdot 2^{43}$

$7 \times 21 \times 13 \times 12$

$6 \cdot 2^{43}$

Q. 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

21×13×12×3

7⋅243

7×21×13×12

6⋅243

Q. 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

$21 \times 13 \times 12 \times 3$

$7 \cdot 2^{43}$

$7 \times 21 \times 13 \times 12$

$6 \cdot 2^{43}$