penny has 25 dimes. she likes to arrange them into three piles, putting an odd number of dimes into each pile. in how many ways could she do this?

Answer 1

10

Answer 2

78

Answer 3

7 ways

Answer 4

i think it is 78 too

Answer 5

Answer = 75
Explanation:-
As information provided in the question,

          Total number of dimes that Penny has = 25 dimes

          Total number of piles in which she likes to arrange the 25 dimes = 3 piles

Now,

      It is given that she wants to put an odd number of dimes into each pile.

Thus,

    Total number of possible pairs of three odd numbers that has a sum of 25 are as:

        {1, 3, 21}, {1, 5, 19}, {1, 7, 17}, {1, 9, 15}, {1, 11, 13}

        {3, 3, 19}, {3, 5, 17}, {3, 7, 15}, {3, 9, 13}, {3, 11, 11}

        {5, 5, 15}, {5, 7, 13}, {5, 9, 11}

        {7, 7, 11}, {7, 9, 9}

Now,

      There are total 15 pairs in which 10 pairs have all three difinite elements and 5 pairs have two identical elements in each pair.

Therefore,

       The number of ways in which we can arrange each pair which has all three distinct elements = 6 ways

And, The number of ways in which we can arrange each pair which has two identical elements elements = 3 ways 

Therefore,

      Total number of ways in which Penny can arrange all 25 dimes into three piles = 10 x 6 + 5 x 3

                                                                                                                                   = 60 + 15

                                                                                                                                   = 75 ways