vanam52923 wrote:
its not permuation,so why are we dividing
When something
is a permutation, you never divide. If you're solving a permutation question, you're putting things in order: "In how many different orders can Amir, Betty and Carlos line up at a ticket window?" is a permutation problem. The answer is 3*2*1 = 6 (we do not divide by anything).
You only divide when the order of things does not matter. In general, if the order of k things doesn't matter, you can count by first pretending order does matter, then dividing by k! at the end. So in your siblings question, the order of the four siblings we choose does not matter -- we aren't picking, say, a President, a Vice-President, a Secretary and a Treasurer. Because the order of our 4 selections does not matter, we can first pretend it does -- we have 16 choices for the first sibling, 14 for the next, 12 for the next and 10 for the final one, so (16)(14)(12)(10) choices in total -- but we then need to divide by 4!, because the order of the four siblings is not supposed to be important.
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