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.

Question

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.

anonymous · Answer

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 · Answer

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 $1/14$.