Question 1185063
i. Determine the number of ways in which the committee may be
formed if it is to contain exactly one women.<pre>
Choose the 1 woman any of C(4,1)=4 ways.
Choose the 3 men any of C(8,3)=56

Answer: {{{(4)(56)}}}{{{""=""}}}{{{matrix(1,2,224,WAYS)}}}
</pre>
ii. Find the probability that at least one women is selected onto the
committee.<pre>
We find the probability that no women (i.e., all men) are chosen, then
subtract from 1.

Number of ways to select all men:  C(8,4)=70 ways
Number of ways to select any 4 people regardless of sex:  C(12,4)=495 ways.

P(all men) = 70/495 = 14/99

P(at least one woman) = 1-14/99 = 99/99-14/99 = 85/99.

Edwin</pre>