Problem 3 [15 pts]: Souvenir Key-chain Bins For each of these problems, write down the permutation/combination...

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Problem 3 [15 pts]: Souvenir Key-chain Bins For each of these problems, write down the permutation/combination expression and then sim- plify to a final number. Alice (she/her) and Bob (he/him) are going souvenir hunting during Spring Break. They come across a store that sells all sorts of key-chains. i. If they buy 75 key-chains, and have six bags to store the key-chains, how many different ways can the key-chains be assigned to the bags? ii. Assume that they pick 19 "Sunny Miami key-chains and only these 19 key-chains. Both Alice and Bob really like this key-chain, so they want each of the six bags to have at least two of them. How many different ways can the "Sunny Miami" key chains be assigned to the bags? iii. Assume they buy 32 "Ft. Lauderdale" key chains and want to distribute them in six bags, one for each friend. They want to make sure everyone has at least 3 key-chains, but no more than 9 key-chains. How many ways can they assign the key chains to the bags given these restrictions? Problem 3 [15 pts]: Souvenir Key-chain Bins For each of these problems, write down the permutation/combination expression and then sim- plify to a final number. Alice (she/her) and Bob (he/him) are going souvenir hunting during Spring Break. They come across a store that sells all sorts of key-chains. i. If they buy 75 key-chains, and have six bags to store the key-chains, how many different ways can the key-chains be assigned to the bags? ii. Assume that they pick 19 "Sunny Miami key-chains and only these 19 key-chains. Both Alice and Bob really like this key-chain, so they want each of the six bags to have at least two of them. How many different ways can the "Sunny Miami" key chains be assigned to the bags? iii. Assume they buy 32 "Ft. Lauderdale" key chains and want to distribute them in six bags, one for each friend. They want to make sure everyone has at least 3 key-chains, but no more than 9 key-chains. How many ways can they assign the key chains to the bags given these restrictions?