Permutation and CombinationHard
Question
A box contains 6 balls which may be all of different colours or three each of two colours or two each of three different colours. The number of ways of selecting 3 balls from the box (if ball of same colour are identical), is:
Options
A.60
B.31
C.30
D.None
Solution
Case -I If all are different then no. of ways is
= 6C3 = 20
Case-II If three each of two colours, then
combination is
2 1 0 → 3!
1 1 1 → 1! = 3! + 1! = 7ways
Case-III If two each of three colours, then
combination is
3 0 → 2!
2 1 → 2! = 2! + 2! = 4 ways
Hence required no.is = 20 + 7 + 4 = 31
= 6C3 = 20
Case-II If three each of two colours, then
combination is
2 1 0 → 3!
1 1 1 → 1! = 3! + 1! = 7ways
Case-III If two each of three colours, then
combination is
3 0 → 2!
2 1 → 2! = 2! + 2! = 4 ways
Hence required no.is = 20 + 7 + 4 = 31
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