The number of different ways in which five alike dashes and eight alike dots can be arranged, using only seven of these ‘dashes’ and ‘dots’ is equal to

Step-by-step solution

Dashes 5 Dots 8 Arrangements 5 2 C 2 7 4 3 C 3 7 3 4 C 4 7 2 5 C 5 7 1 6 C 6 7 0 7 C 7 7 Required number of ways = C 2 7 + C 3 7 + C 4 7 + C 5 7 + C 6 7 + C 7 7 = 2 7 - 7 - 1 = 120