Your goal is to collect all 80 player cards in a game. The Player cards are...

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Your goal is to collect all 80 player cards in a game. ThePlayer cards are numbered 1 through 80. High numbered cards arerarer/more valuable than lower numbered cards.
Albert has a lot of money to spend and loves the game. So everyday he buys a pack for $100. Inside each pack, there is a randomcard. The probability of getting the n-th card isc(1.05)^-n, For some constant c. Albert buys his firstpack on June 1st. What is the expected number of Player cardsAlbert will collect in June?(30 days)
a.) Find an exact, closed-form expression for c. (Answer shouldnot include a summation symbol or integral sign).
b.)Find the expected number of unique Player cards Albert willcollect in June. (Answer may include summation symbol or integralsign.

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A Everyday when Albert buys the pack there will be a card inthe pack with a random number between 1 and 80 written on it Henceeveryday following relation will hold sum of probabilities ofobtaining n th card will be 1On See Answer

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