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A bank contains pennies, nickels, dimes, quarters and half-dollars. How many different...

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thi-dallas | Student, Undergraduate | Valedictorian

Posted August 10, 2013 at 7:45 PM via web

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A bank contains pennies, nickels, dimes, quarters and half-dollars. How many different sets of three coins can be formed?

(PS. As the answer is given to be 35, it is assumed that 7 coins are present in the bank.)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 10, 2013 at 7:52 PM (Answer #1)

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The problem does not specify the total number of coins. If the total number of pennies, nickels, dimes, quarters and half-dollars in the bank is equal to n, the number of sets of three coins that can be formed is given by C(n, r) = `(n!)/(r!*(n-r)!)`

If the total number of coins in the bank is 7, C(7,3) = `(7!)/(3!*(7-3)!) ` = `(7*6*5*4)/(4*3*2*1)` = 35

The total number of sets of 3 coins that can be formed given 7 coins in all is 35.

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