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05 Jan 2005, 01:25
Kudos
Bookmarks
Hi,
During my practice I came across this question:
In a class of 20 students, what is the ratio of the number of groups of 5 students to the number of groups of 4 students that can be formed.
I came down to the equation where:
# of groups of 5 students = 20*19*18*17*16/5*4*3*2*1
# of groups of 4 students = 20*19*18*17/4*3*2*1
My question is lets say I have already spent 30 seconds getting to this equation.
Do I actually have to multiply out each of these (e.g. multiply 20*19*18*17*16 and then divide it by 120) and then repeat the same for the #4 student groups, or is there a quicker way to solve this problem?
I would get freaked out on time if I had to sit and multiplt 20*19*18*17*16
Any suggestions?
Thanks
andy
During my practice I came across this question:
In a class of 20 students, what is the ratio of the number of groups of 5 students to the number of groups of 4 students that can be formed.
I came down to the equation where:
# of groups of 5 students = 20*19*18*17*16/5*4*3*2*1
# of groups of 4 students = 20*19*18*17/4*3*2*1
My question is lets say I have already spent 30 seconds getting to this equation.
Do I actually have to multiply out each of these (e.g. multiply 20*19*18*17*16 and then divide it by 120) and then repeat the same for the #4 student groups, or is there a quicker way to solve this problem?
I would get freaked out on time if I had to sit and multiplt 20*19*18*17*16
Any suggestions?
Thanks
andy
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06 Jan 2005, 02:55
Kudos
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Paul
but take it one step further and it's even simpler. We want the ratio of these two numbers. The first is 20x19x18x17x16/5x4x3x2x1 and the second is 20x19x18x17/4x3x2x1.
Just keep them exactly like that, and put one over the other to form the ratio. Now do the division, and the bottom one (the number of 4 person groups) will be flipped around and multiplied by the top one.
NOW EVERYTHING CANCELS OUT.
After all that, the only thing left is 16/5.
Done in 15 seconds.
