Ray and Lilli are designing their own shoes. They have 4 color options for the base and 6 color options for the accent. They can also pick between 2 fonts for the embroidery. What is the probability that Ray and Lilli design identical shoes?


Remark: in the solution, the word Combination is used in the daily usage of the word, not in the combinatorial (mathematical) language.


Let the available 4 base colors be {b_1, b_2, b_3, b_4},

the available 6 accent colors be   {a_1, a_2, a_3, a_4, a_5, a_6},

and the available 2 fonts for the embroidery be {e_1, e_2},


so we have 4 b's, 6a's and 2 e's.


The event that Ray and Lilly design identical shoes can happen in the following way:

Ray has in total 4*6*2=48 possible combinations, and in each of these combinations, Lilly makes the same exact combinations of the 3- b's, a's and  e's.

The sample space is 48 possible combinations of Ray * 48 possible combinations of Lilly = 48*48
(among these there are 48 matches of the combinations)



Thus P(designing identical shoes)=48/(48*48)=1/48=0.02



Answer:0.02




Rate answer
Wrong answer?

If your question is not fully disclosed, then try using the search on the site and find other answers on the subject Mathematics.

Find another answers

Load image