• anonymous
A club with ten members wants to choose a president, vice-president, secretary, and treasurer. Six of the members are women, and four are men.What is the probability that all officers will be women? WORK PLEASE!! This is a permutation.
  • Stacey Warren - Expert
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  • jamiebookeater
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  • anonymous
probability umm....... this is the ans.... Out of 10 members, 6 are women. The probability that all 4 officers will be women is: 6/10x5/9x4/8x3/7=360/5040=1/14
  • KingGeorge
I would also like to mention the way I like best. You need to find the number of ways that 4 women can be chosen from a group of 6 women, and find how many total groups exist that can be formed. This is given by \[\Large {{6 \choose 4} \over {10 \choose 4}}={15 \over 210}={1 \over 14}\]So once again, we get a probability of \(1/14\).

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