There are 6 possible combinations of choosing 2 boys and 2 girls:
0 = girl
1 = boy
0011
0101
0110
1001
1010
1100
Each of these has a probability of 1/10
worked out by:
(3 x 3 x 2 x 2)/(6 x 5 x 4 x 3) = 1/10
6 x 1/10 = 3/5
Probability
-
Mathsbuddy
- Master | Next Rank: 500 Posts
- Posts: 447
- Joined: Fri Nov 08, 2013 7:25 am
- Thanked: 25 times
- Followed by:1 members
-
Mathsbuddy
- Master | Next Rank: 500 Posts
- Posts: 447
- Joined: Fri Nov 08, 2013 7:25 am
- Thanked: 25 times
- Followed by:1 members
A brief explanation of why each probability is 1/10:
Look at combination BBGG
p1 = p(1st choice is boy) = 3/6
p2 = p(2nd choice is boy) = 2/5
p3 = p(3rd choice is girl) = 3/4
p4 = p(4th choice is girl) = 2/3
p1 AND p2 AND p3 AND p4 = 3/6 * 2/5 * 3/4 * 2/3 = (3 * 2 * 3 * 2)/(6 * 5 * 4 * 3)
Note that for all combinations listed previously, the numerator will be the same (just multiplied in a different order). Also, the denominator will be the same.
The result is 36/360 = 1/10
Then 6 combinations * 1/10 = 3/5
Look at combination BBGG
p1 = p(1st choice is boy) = 3/6
p2 = p(2nd choice is boy) = 2/5
p3 = p(3rd choice is girl) = 3/4
p4 = p(4th choice is girl) = 2/3
p1 AND p2 AND p3 AND p4 = 3/6 * 2/5 * 3/4 * 2/3 = (3 * 2 * 3 * 2)/(6 * 5 * 4 * 3)
Note that for all combinations listed previously, the numerator will be the same (just multiplied in a different order). Also, the denominator will be the same.
The result is 36/360 = 1/10
Then 6 combinations * 1/10 = 3/5
Last edited by Mathsbuddy on Tue Nov 12, 2013 8:41 am, edited 2 times in total.
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
If you're interested, we have a free video on calculating combinations (like 6C4) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789stephny wrote:please break down your calculation of 6C4 and how that equals 15
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
Mathsbuddy
- Master | Next Rank: 500 Posts
- Posts: 447
- Joined: Fri Nov 08, 2013 7:25 am
- Thanked: 25 times
- Followed by:1 members
There are 6 possible combinations of choosing 2 boys and 2 girls:
0 = girl
1 = boy
0011
0101
0110
1001
1010
1100
Each of these has a probability of 1/10
worked out by:
(3 x 3 x 2 x 2)/(6 x 5 x 4 x 3) = 1/10
6 x 1/10 = 3/5
0 = girl
1 = boy
0011
0101
0110
1001
1010
1100
Each of these has a probability of 1/10
worked out by:
(3 x 3 x 2 x 2)/(6 x 5 x 4 x 3) = 1/10
6 x 1/10 = 3/5
-
Mathsbuddy
- Master | Next Rank: 500 Posts
- Posts: 447
- Joined: Fri Nov 08, 2013 7:25 am
- Thanked: 25 times
- Followed by:1 members
There are 6 possible combinations of choosing 2 boys and 2 girls:
0 = girl
1 = boy
0011
0101
0110
1001
1010
1100
Each of these has a probability of 1/10
worked out by:
(3 x 3 x 2 x 2)/(6 x 5 x 4 x 3) = 1/10
6 x 1/10 = 3/5
0 = girl
1 = boy
0011
0101
0110
1001
1010
1100
Each of these has a probability of 1/10
worked out by:
(3 x 3 x 2 x 2)/(6 x 5 x 4 x 3) = 1/10
6 x 1/10 = 3/5
