Question

How many ways eight tigers in a cage be fed with three small wild animals, three small goats and two domestic fowls?​

Answer 1

The 8 tigers in the cage can be fed in 560 ways.

Given

• There are 8 tigers to be fed
• They are to be fed with three small wild animals, three small goats, and two domestic fowls

To Find

The number of ways in which the tigers can be fed.

Solution

Total number of prey

no. of small wild animals + no. of small goats + no. of domestic fowls

= 3 +3  + 2

= 8

Since there are 8 tigers, every tiger gets one prey

Now 3 wild animals can be distributed in ⁸C₃ ways

Now there are 5 tigers to be fed.

The 3 small goats can be given out in ⁵C₃ ways

Now, there are 2 tigers to be fed

They can be fed in ²C₂ ways

Therefore total no.of ways to feed the tigers are

⁸C₃ X ⁵C₃ X ²C₂

We know that ⁿCₓ = n!/((n-x)! X x!) Using this we get,

= $\frac{8!}{3! X 5!} X \frac{5!}{3! X 2!} X \frac{2!}{2!}$

Expanding the numerator we get,

= $\frac{8 X 7 6 X 5!!}{3 X 2 X 5!} X \frac{5 X 4 X 3!}{3! X 2} X 1$

canceling the common terms out gives us

= $8 X 7 X 5 X 2$

= 560

Therefore, the 8 tigers in the cage can be fed in 560 ways.

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