Part B Jane has 5 rings. In how many distinct ways can she put them on her finge

Question

Part B Jane has 5 rings. In how many distinct ways can she put them on her fingers? Assume first that the rings are distinct Assume that there is no restriction on how many rings she uses, from none to 5, and there is no restriction how many rings can be put on one finger. The order of multiple rings on one finger is irrelevant. Assume that all 5 rings are used, but no two rings can be worn on one finger. Assume now that rings are indistinguishable, just identical bands. Assume that there is no restriction on how many bands she uses, from none to 5. and there is no restriction how many bands can be put on one finger. Assume that Jane uses all 5 bands and each finger must have at most one band.

Explanation / Answer

Part 1

Lets assume that number of bands on a finger=xi

Hence x1+x2+x3+-----------------+x10<=5

Hence as there is no restriction on the number of bands worn.Jane can wear 0,1,2,3,4,5 bands

Hence number of ways=(10+5-1)C(10-1) +13C9+12C9+11C9+10C9+9C9=3003 ways

Part 2

She has 5 bands and 10 fingers and each finger can have atmost one band

hence it is simple like selecting 5 fingers from 10 fingers=10C5 =252 ways

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