number of ways in which 5 identical red balls, 3 identical green balls can be arranged in a row is __
Answers
Answer:
There are 11 spaces.
Number of ways of placing 5 identical red balls in 11 spaces: 11C5 = 11!/(5!*6!) = 462
Once we place all the 5 red balls, say in first of the 462 possible combinations, there is only one way to arrange the 6 green balls (as they are identical)
By this logic final answer: 11C5 * 1 = 462
We can also start by arranging green balls first
11C6 * 1 = 11!/(6!*5!) * 1 = 462
Answer: 462 ways.
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Answer:
These are totally 9 balls of which 2 are identical of one kind, 3 are a like of another kind and 4 district ones.
At least one ball of same color separated = Total − No ball of same color is separated
Total permutation =
2!3!
9!
For no ball is separated : we consider all balls of same color as 1 entity, so there are 3 entities which can be placed in 3! ways.
The white and red balls are identical so they will be placed in 1 way whereas green balls are different so they can be placed in 4! ways
⇒Req=3!×4!
At least one ball is separated =
2!3!
9!
−3!4!
=
2×6
9×8×7!
−6×4!
=6(7!)−6(×4!)
=6(7!−4!).
Hence, the answer is 6(7!−4!).