Find the total number of ways in which 10 different cakes can be divided into two parcels each containing the same number ?

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2 parcels each containing same number of cakes, then each partition must contain 5 cakes each.

10 different cakes we choose 5 for a parcel, then the remaining 5 go into the other parcel.

Total number of ways $= C(10,5)= 252$

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