give the following from the question:
the organizer will select from 3 workshop about anthropology and 10 workshops about psychology.
we were asked in how many ways she can select 7 workshops if 2 or fewer must be anthropology
so,
If 2 or fewer must be anthropology,
Then tha means it is either she selects 2 from anthropology and 5 from psychology or 1 from anthropology and 6 from psycology.
that is:
= 3C2 x 10C5 or 3C1 x 10C6
= 3!/(3-2)!2! x 10!/(10-5)!5! + 3!/(3-1)!1! x 10!/(10-6)!6!
= 3x2!/2! x 10x9x8x7x6x5!/5!5! + 3x2!/2! x 10x9x8x7x6!/4!6!
= 3 x 252 + 3 x 210
= 756 + 630
= 1,386 ways
The ways she can select 7 workshops if 2 or fewer must be about anthroplogy is 1,386 ways
