Question

a group of mathematics faculty at the local college consists of 8 women and 10 men. three people are to be selected to go to a conference. how many different ways can a group of three people be selected from this group of 18? in how many ways can three women be chosen from the group of 8 women? what is the probability that all women will be chosen to attend the conference? enter as decimal rounded to the nearest hundredth.

Explanation:

Step1: Calculate total ways to select 3 from 18

Use combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 18$ and $r=3$.
$C(18,3)=\frac{18!}{3!(18 - 3)!}=\frac{18\times17\times16}{3\times2\times1}=816$

Step2: Calculate ways to select 3 from 8 women

Use combination formula with $n = 8$ and $r = 3$.
$C(8,3)=\frac{8!}{3!(8 - 3)!}=\frac{8\times7\times6}{3\times2\times1}=56$

Step3: Calculate probability

Probability $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.
$P=\frac{C(8,3)}{C(18,3)}=\frac{56}{816}\approx0.07$

Answer:

816
56
0.07