how many possible mismatched combinations can there be with 46 pairs of shoes

Question

a girl has 46 pairs of shoes, someone suggested she could have more if she was to mismatch them....how many possible pairs of shoes would there be?

 

Answer 1

or you can think like this

 

you have 46 shoes for the right leg,and 46 for the left.

 

for the right leg ,you can choose any one of the 46 available in 46 ways.

now for the left leg,you dont want to make it a matching pair,

so choose out of the remaining 45 in 45 ways.

 

total number of ways then will be 46* 45

which is 2070

Answer 2

Hello Donna,

 

46 pairs of shoes is the same as having 46 shoes for the Left and 46 for the Right leg. In order to geta wearable pair we need to select 1 of 46 of the left (46 ways) and 1 of 46 for the right (46 ways) thus the total number of pairs is 46 x 46 = 2116. Of these 46 pairs are matched and the remaining 2070 are mismatched.

 

I can provide Online tutoring.

 

Wishing you the best,

Pradip M