Let's visit a Zoo!
Mrs. Smith the teacher decides to take her class on a trip to the zoo. When they all came at the zoo, Mrs. Smith took 3 children at a time to the lion's cage as often as she can, but she did not take the same 3 children to the lion's cage more than once. After everyone visited the lion's cage, she found that she had gone to the lion's cage 84 times more than a particular child. If the number of children in her class is what is the value of
Note: Each child takes as many visits as possible to the lion's cage.
The answer is 15.
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1 solution
There are C(N,3) possible groups of 3 children. This is the maximum possible number of trips to the zoo that avoids duplication of any group of 3 children.Now of these C(N,3) trips, (all of which the teacher supervises), each child will be a member of C(N-1,2) of them.
Thus we need to find N such that C(N-1,2) + 84 = C(N,3). ASA, (After Some Algebra), we end up with the equation
(N - 1) * (N - 2) * (N - 3) = 504.
Now 504 = 7 * 8 * 9, so N - 1 = 9 and thus N = 10.
The desired answer is then 10 + 5 = 1 5 .