Barrons 2400 Question

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<p>In the permutations combinations chapter of the 2400 book (page 222 if you have it near you) says on the combinations, if order is irrevelevant you divide number of combinations by r!, which makes sense since order is irrelevant. but then at the end of the chapter in the review questions (number 10 page 230) it says to times the total number of combinations by r!</p>

<p>heres what it says for those of you who don't have it...</p>

<p>calculate number of 3 person committees made up of 6 willing people. so you would do 6x5x4 to get 120, and since order doesn't matter, it says you must divide by 3x2x1.</p>

<p>on the review test it says...
6 chairs are placed in a row to seat 6 people. how many arrangements are possible if two of the people insist on sitting next to eachother? so that means 4 seats and 4 people are up for different combos, so 4x3x2x1 gives you 24, and since there are 5 pairs of seats in which the two people who would be sitting next to eachother would be, you times 24 by 5 to get 120. Then it says because of the fact that the two people could be sitting in any order, you multiply by 2.</p>

<p>can someone explain to me the difference in these two processes? they appear to be asking you the same thing in both, but they do them in a manner that suggests otherwise....yea i'm pretty confused...help please...</p>

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<p>just as you said, in the first question the order is not important unlike in the second question.<br>
when you see the word <arrrangments> it means, for example, not just randomly dumping a bunch of books in a box, but arranging them on a shelf, so the order becomes important.
picking 3 different books out of 6 and arranging them on a shelf can be done 6x5x4=120 different ways.
picking 3 different books out of 6 and dropping them in a box you count each set of 3 picked out books (say, A,B,C) only once instead of 3x2x1=6 times (ABC, ACB, BAC, BCA, CAB, CBA). 120/6=20 different ways of choosing.</arrrangments></p>

<p>in the second question two finicky people A and B could seat on the chairs 1&2, 2&3, 3&4, 4&5, or 5&6.
For each arrrangement out of these 5 they could seat in AB or BA order, which makes 5x2=10 different arrangements.
for each of their arrangements you seat 4 remaining people on 4 remaining chairs 4x3x2x1=24 different ways. total = 24x10=240.
i just did it in a different order than barrons. order did not matter, get it? lol</p>

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<p>thanks very much man</p>

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<p>my pleasure</p>