Q. 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
NTA AbhyasNTA Abhyas 2022
Solution:
Dashes 5
Dots 8
Arrangements
5
2
${ }^{7} C_{2}$
4
3
${ }^{7} C_{3}$
3
4
${ }^{7} C_{4}$
2
5
${ }^{7} C_{5}$
1
6
${ }^{7} C_{6}$
0
7
${ }^{7} C_{7}$
Required number of ways $={ }^{7} C_{2}+{ }^{7} C_{3}+{ }^{7} C_{4}+{ }^{7} C_{5}+{ }^{7} C_{6}+{ }^{7} C_{7} $
$=2^{7}-7-1=120$
| Dashes 5 | Dots 8 | Arrangements |
|---|---|---|
| 5 | 2 | ${ }^{7} C_{2}$ |
| 4 | 3 | ${ }^{7} C_{3}$ |
| 3 | 4 | ${ }^{7} C_{4}$ |
| 2 | 5 | ${ }^{7} C_{5}$ |
| 1 | 6 | ${ }^{7} C_{6}$ |
| 0 | 7 | ${ }^{7} C_{7}$ |