Question

plz solve the probability question

Answer 1

1) The total number of outcomes in the word probability = 11!.

2) Given that there are 3 letters in between them.

If P is in the 1st position, Then L would be in the 5th position.

If P is in the 2nd position, Then L will be in the 6th position.

There are 7 such positions, the last one having P in the 7th position and L in the last position.


3) If L is in the 1st position, Then P is in the 5th position.

There are 7 such positions, The last one having L in the 7th position and P in the Last position.

Up to now, we have filled in 2(P and L) of the 11 letters in 7 + 7 = 14 ways.


4) The remaining 9 letters can be filled themselves in 9! ways.


The probability that the P and L letters have exactly 3 letters

= 14 * 9!/11!

= 14 * 9 * 8 * 7 * 6 * 5 * 4 * 3  * 2 * 1/ 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

= 14/11 * 10

= 14/110.


Hope this helps!