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A set of 10 flags, 5 red, 3 blue and 2 yellow are to be arranged in a line along a balcony. If flags of the same colour are INDISTINGUISHABLE, find the number of arrangements in which,

1) The three blue flags are together
2) The yellow flags are not together
3) The red flags occupy alternate positions in the line
4) If there is room for only 9 of the flags, find the total number of possible arrangements.

https://brainmass.com/math/combinatorics/permutations-11359

Solution Preview

1) The three blue flags are together

We can consider the 3 blue flags to be 1
Remaining flags
Red= 5
Yellow= 2

Total=1+5+2= 8

Total no of arrangements= 8!= 40320 when the flags are distinguishable

But out of these 5! Arrangements of red flags and 2! Permutations of yellow flags are indistinguishable

Hence total no of arrangements=8!/(5!* 2!)= 168