ONE EIGHTH CONTEST 2025
St. Peter's SHS - 38 points
Osei Kyeretwie SHS - 38 points
Okuapemman School - 37 points
ONE EIGHTH CONTEST 2025
University Practice SHS - 43 points
Ghana SHS, Koforidua - 38 points
Winneba SHS - 30 points
ONE EIGHTH CONTEST 2025
Mawuli School - 48 points
Armed Forces SHTS - 38 points
Berekum Presby SHS - 33 points
ROUND 5
TIE BREAKER
TIE BREAKER
QUESTION
Find the number of ways of selecting 6 men and 6 women from a group of 8 men and 7 women
SOLUTION
$={}_{6}^{8}C\times{}_{6}^{7}C$
$=28\times 7$
$=196$
PRACTICE QUESTIONS
1. In how many ways can a committee of 3 men and 2 women be selected from 5 men and 4 women?
ANSWER: 60
SOLUTION
$\text{Ways to choose the men}=\binom{5}{3}=10$
$\text{Ways to choose the women}=\binom{4}{2}=6$
Multiply the choices:
$10\times6=60$
2. In how many ways can a committee of 2 men and 3 women be selected from 6 men and 5 women?
ANSWER: 150
SOLUTION
$\text{Ways to choose the men}=\binom{6}{2}=15$
$\text{Ways to choose the women}=\binom{5}{3}=10$
Multiply the choices:
$15\times10=150$
3. In how many ways can a committee of 4 men and 1 women be selected from 7 men and 3 women?
ANSWER: 105
SOLUTION
$\text{Ways to choose the men}=\binom{7}{4}=35$
$\text{Ways to choose the women}=\binom{3}{1}=3$
Multiply the choices:
$35\times3=105$
4. In how many ways can a committee of 3 men and 3 women be selected from 8 men and 6 women?
ANSWER: 1120
SOLUTION
$\text{Ways to choose the men}=\binom{8}{3}=56$
$\text{Ways to choose the women}=\binom{6}{3}=20$
Multiply the choices:
$56\times20=1120$
5. In how many ways can a committee of 2 men and 2 women be selected from 4 men and 4 women?
ANSWER: 36
SOLUTION
$\text{Ways to choose the men}=\binom{4}{2}=6$
$\text{Ways to choose the women}=\binom{4}{2}=6$
Multiply the choices:
$6\times6=36$
6. In how many ways can a committee of 4 men and 2 women be selected from 9 men and 5 women?
ANSWER: 1260
SOLUTION
$\text{Ways to choose the men}=\binom{9}{4}=126$
$\text{Ways to choose the women}=\binom{5}{2}=10$
Multiply the choices:
$126\times10=1260$