Permutations
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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.
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Solution Summary
Finds the number of arrangements
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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
Answer= 168
2) The yellow flags are not together
We can first consider the case where the ...
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