Here's 9 (i.e powers 3 + 2 + 4 = 9) objects in the expression a3 b2 c4 and there are 3 a’s, 2 b’s, 4 c’s
Therefore by using the formula,
n!/ (p! × q! × r!)
The total number of arrangements = 9! / (3! 2! 4!)
= [9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1] / (3 × 2 × 1 × 2 × 1 × 4 × 3 × 2 × 1)
= 7 × 6 × 5 × 3 × 2 × 1
= 1260