S1 statistics...pls help!!!

the question is:
a bag contains 30 plastic tiles which are used in a word game. each tile has a single letter written on it. 12 of the tiles have vowels written on them and the remaining 18 tiles have consonants written on them. a contestant in the game picks 7 tiles at random, without replacement.
(i) find the probability that, of the 7 tiles, 4 have vowels written on them and 3 have consonants written on them.
(ii) find the probability that, of the 7 tiles at least 1 has a vowel written on it.
(iii) the letters written on the tiles are A B A E S S U. calculate the number of different possible arrangements of these letters if the tiles are arranged in a straight line.
i know i should kno how to do this by now but... :confused:

Reply 1

Libertine

louie2lene

(Number of ways of selecting 4 tiles from 12*Number of ways of selecting 3 tiles from 18)/Number of ways of selecting 7 tiles from 30
= (12C4 x 18C3)/30C7

louie2lene

(ii) find the probability that, of the 7 tiles at least 1 has a vowel written on it.

= 1 - P(selecting 7 consonants)
= 1 - 18/30*17/29*16/28*...*12/24

louie2lene

(iii) the letters written on the tiles are A B A E S S U. calculate the number of different possible arrangements of these letters if the tiles are arranged in a straight line.

= Total number of arrangements/total number of repeats
= 7!/(2! x 2!)