Question

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

• A. $350$
• B. $120$
• C. $1287$
• D. None of these

Answer 1

Answer: (B)

$120$

We have _ _ _ _ _ _ _ dash and $8$ dots,

We need to arrange $7$ out of these $13$

we can have $5$ dash $2$ dots

or $4$ dash $3$ dots

$3$ dash $4$ dots

$2$ dash $5$ dots

$1$ dash $6$ dots

$0$ dash $7$ dots.

$={}^7{C}_5+{}^7{C}_4+{}^7{C}_3+{}^7{C}_2+{}^7{C}_0$

$=120$ ways.

Hence, the answer is $120.$