Question

There are 15 stones placed in line numbered 1 to 15. In how many ways a person can mark 5 of these stones so that there are an odd number of stones between any two stones marked:-

• A. 77
• B. 56
• C. 252
• D. 21

Answer 1

The correct option is A 77

Total no. of ways of marking the stones is ${}^{15}{\text{C}}_5$

If we want odd number of stones between any two stones marked

We can place the stones in two types of ways

At least 1 stone should be there in between two marked stones

Therefore placing in odd numbered places i.e. ${}^8{\text{C}}_5$

And placing in even numbered places i.e. ${}^7{\text{C}}_5$

By this method we will have at least 1 stone between 2 marked stone i.e. odd no. of stones

${\therefore }^8{\text{C}}_5{+}^7{\text{C}}_5=77$

Answer