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Question 10 : Out of 13 objects, 4 are indistinguishable and rest are distinct. The number of ways we can choose 4 objects out of 13 objects is __________.

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Video Explanation

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Explanatory Answer

Since there are indistinguishable toys, only the number of such indistinguishable toys picked matter.
We may choose
0 indistinguishable toys & 4 distinct toys
1 indistinguishable toys & 3 distinct toys
2 indistinguishable toys & 2 distinct toys
3 indistinguishable toys & 1 distinct toys
4 indistinguishable toys & 0 distinct toys

So effectively, the number of ways of picking is ,
the number of ways of picking 4 distinct toys + the number of ways of picking 3 distinct toys + the number of ways of picking 2 distinct toys + the number of ways of picking 1 distinct toys + the number of ways of picking 0 distinct toys.
There are 13 - 4 = 9 distinct toys.
Therefore, the number of ways of picking = ⁹C₄ + ⁹C₃ + ⁹C₂ + ⁹C₁ + ⁹C₀ = 126 + 84 + 36 + 9 + 1 = 256

The question is " out of 13 objects, 4 are indistinguishable and rest are distinct. The number of ways we can choose 4 objects out of 13 objects is __________. "

Hence, the answer is 256

 

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