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# S1 Permutations and Combinations watch

1. Hi, these are part of my homework questions (the other parts and questions I've been able to do myself), which I was given the answers to. So I'm not looking for easy answers, I honestly have no clue how to work them out.

1.) A set of 8 square tiles, identical in every way except colour, are to be arranged in a straight line. Given that 3 are red, 3 are black and 2 are white, calculate:

(iii.) the number of arrangements in which the 2 white tiles have exactly 2 tiles, one red and the other black, between them.

2.) There are 4 white wines and 4 red wines, incuding one red wine called "Rot". The wines ranked 1st to 4th are graded "A" and the wines ranked 5th to 8th are graded "B".

(ii.) Find the nmber of ways in which the 4 red wines are all of the same grade.

(iii.) Among the numbe rof ways in which all the red wines are of the same grade, find the number in which "Rot" was ranked 1st overall.

3.) Calculate the total number of different permutations of all the letters A, B, C, D, E, F when

(ii.) the letters A to B are to be adjacent to one another- is it 5!x 2!?

(iii.) The first letter is A, B, or C and the last letter is D, E, or F

4.) Eight cards, bearing the letters P,A,R,A,L,L,E,L are placed in a box. 3 cards are drawn out at random without replacement. Calculate the probability that :

(ii.) the 3 cards bear the letters A, L, E in that order- how do you ensure they're in that order?

(iii.) the 3 cards bear the letters A,L,E in any order

(iv.) the first 2 cards bear different letters.
2. 8!/3!3!2!=8*7*5*2=560 total number of arrangements.

So for 1 iii)

We can have
WBRWXXXX (x2) (probability (2*3*3*2)*2
XWBRWXXX (x2)
XXWBRWXX (x2)
XXXWBRWX (x2)
XXXXWBRW (x2)
(x2) as BR or BR doesn't matter
Spoiler:
Show

64*5=320 so

320/560=4/7 is my answer after a bottle of wine

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Updated: January 29, 2010
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