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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.

    © BrainMass Inc. brainmass.com November 29, 2021, 11:57 pm ad1c9bdddf
    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

    Answer= 168

    2) The yellow flags are not together

    We can first consider the case where the ...

    Solution Summary

    Finds the number of arrangements

    $2.49

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