Permutation Question (1 Viewer)

Arucerious · Oct 28, 2015

I'm new to perms and comms so how do I do Q7)B-D and while I'm at it, what formula do you use for those type of questions with restrictions?

InteGrand · Oct 28, 2015

Arucerious said:
I'm new to perms and comms so how do I do Q7)B-D and while I'm at it, what formula do you use for those type of questions with restrictions?

$(b) If the two S's are together, we treat the pair of S's as one unit:$

$[SS] O C K .$

$So this becomes like arranging four distinct letters in a row, which can be done in $4!$ ways, so the answer is $4!=24$.$

$(c) The two S's are separated by at least one other letter if and only if they are \textsl{not} together. Since the total no. of words without restriction is $\frac{5!}{2!}=60$, and the total no. of words \textsl{with} the two S's together is 24 (from above), the answer to this question is no. of all remaining words, i.e. $60-24 = 36$.$

$(d) Note that in half the words, K is left of C, and in the other half, C is left of K. So the answer to this is just half the total no. of words, i.e. answer is $\frac{1}{2}\times 60 = 30$.$

Arucerious · Oct 28, 2015

InteGrand said:
$(b) If the two S's are together, we treat the pair of S's as one unit:$

$[SS] O C K .$

$So this becomes like arranging four distinct letters in a row, which can be done in $4!$ ways, so the answer is $4!=24$.$

$(c) The two S's are separated by at least one other letter if and only if they are \textsl{not} together. Since the total no. of words without restriction is $\frac{5!}{2!}=60$, and the total no. of words \textsl{with} the two S's together is 24 (from above), the answer to this question is no. of all remaining words, i.e. $60-24 = 36$.$

$(d) Note that in half the words, K is left of C, and in the other half, C is left of K. So the answer to this is just half the total no. of words, i.e. answer is $\frac{1}{2}\times 60 = 30$.$

For question (d), I don't understand how you know that in half of the words, K is left of C, and in the other half, C is left of K.

Drsoccerball · Oct 28, 2015

Arucerious said:
For question (d), I don't understand how you know that in half of the words, K is left of C, and in the other half, C is left of K.

Theres two options. It can either be on the right or left therefore 50/50.

InteGrand · Oct 28, 2015

mastermind101 said:
.

Irrelevant to this thread – why post it here?

InteGrand · Oct 28, 2015

BLIT2014 said:
Report it?

Lol I'd forgotten about that feature.

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Permutation Question (1 Viewer)

Arucerious

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InteGrand

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Arucerious

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Drsoccerball

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InteGrand

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InteGrand

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