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  4. Out of 10 white, 8 black and 6 red balls, the number of ways in which one or more balls can be selected is (assuming balls of the same colour are identical)

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Q. Out of $10$ white, $8$ black and $6$ red balls, the number of ways in which one or more balls can be selected is (assuming balls of the same colour are identical)

NTA AbhyasNTA Abhyas 2020Permutations and Combinations

Solution:

Required number of ways
$=\left(10 + 1\right)\left(8 + 1\right)\left(6 + 1\right)-1$
$=11\times 9\times 7-1$
$=693-1$
$=692$