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by MBA.Aspirant » Mon Nov 07, 2011 4:24 pm
There are ten teams in a basketball league. During the season, each team plays the others five times. How many games are played in the basketball league in total?

A: 45
B: 85
C: 125
D: 225
E: 450
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by user123321 » Mon Nov 07, 2011 4:45 pm
if from ten teams each team played against each other once, then number of possibilities are 10c2.
Since they played against each other 5 times. it should be 5*10C2 = 225

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by neelgandham » Wed Nov 09, 2011 1:49 am
There are ten teams in a basketball league. During the season, each team plays the others five times. How many games are played in the basketball league in total?

Number of games played in the basketball league if each team plays the others once = n*(n-1)/2 = (nc2)

How ?

Let the number of teams be 3 a,b,c. Then the number of games played in the basketball league if each team plays the others once = a-b,a-c, b-c = 2+1
Let the number of teams be 4 a,b,c,d. Then the number of games played in the basketball league if each team plays the others once = a-b,a-c,a-d, b-c,b-d, c-d = 3+2+1
...

If the number of teams is n, Then the number of games played in the basketball league if each team plays the others once = n-1 + n-2 + ....1 = (n-1)*(n-1+1)/2 = n*(n-1)/2

back to the problem!

Number of games played in the basketball league if each team plays the others once = n*(n-1)/2 = 10*9/2 = 45
Since they played against each other 5 times, the number of games played in the basketball league = 5*45 = 225

IMO D
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