This relates to combination and permutations and the number of distinct arrangements that are possible will be 6.
From the information, a mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row.
Let 1 = IMO
Let 0 = IPho.
Therefore, the number of arrangement will be:
0011
0110
1100
1010
0101
1001
Therefore, the number of arrangement will be 6.
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