Question

Jayden and Alexa were asked if 6C2 + 6C3 = 7C3 is true. Their calculations showed it was not true, but they both made mistakes in their calculations. Explain and correct their mistakes.
Alexa added the fractions by using the LCD (least common denominator).

Answer 1

First person adds in denominator, step 2 when it's supposed to be multiplication 2!4! = 2*24

720/48 + 720/36 = 7*720/144
multiply everything by 144
144 (720/48 + 720/36) = 7*720
factor 144/48 = 3 and 144/35 = 4

3*720 + 4*720 = 7*720
correct

The other person just writes down the wrong numbers in the denominator of factions when they go to step two.
2!4! = 2*1*4*3*2*1
which does not equal 4*3!3!
there's an extra 3