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Each of A, B, C and D is a positive integer with the proviso that A ≤ B ≤ C ≤ D ≤ 20.

Determine the total number of quadruplets (A, B, C, D) such that A*B*C*D is divisible by 50.

 No Solution Yet Submitted by K Sengupta Rating: 4.0000 (1 votes)

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 Solution | Comment 5 of 11 |
`50 = 2*5*5Let P={5,10,15,20}, q = set of remaining less than 21to be  divisible by 50, at least 2 must be from p.Case 1: 4 chosen from pNo = 1Case 2: 3 chosen from p and 1 from q4C3 * 16 = 4*16 = 64Case 3: 2 from p and 2 from qif chosen = 5,15one from remaining 2 must be even.No = 8*15 = 120(8 ways even can be chosen and remaining in 15 ways)if chosen not equal to 5,15.Total no. of ways 2 chosen p = 4C2 = 6excluding previous case its 5product of these 2 will be divisible by 50 itselfNo = 5*16C2 = 5*8*15 = 600Total = 1+64+120+600 = 785`

 Posted by Praneeth on 2010-08-20 17:29:13

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