How many three digit number can be made with three 4's , four 2's and two 3's?

Answer 1

first of all listing the choices of digits
444 --- can be arranged in 1 way
442--- can be arranged in 3 ways
443--- can be arranged in 3 ways
422--- can be arranged in 3 ways
433--- can be arranged in 3 ways
423--- can be arranged in 6 ways

222--- can be arranged in 1 way
223--- can be arranged in 3 ways
233--- can be arranged in 3 ways

total number of 6(3) + 1 + 6 = 25

check to see if I got them all