Question

In shooting shooting competition a man can score 0 2 9 4 points for each short then the number of different ways in which we can score 14 points in 5 shots is?​

Answer 1

30 Ways in which we can score 14 points in 5 shots.

Explanation:

Since, we have to score 14 in 5 shots using the scores 0,2,9,4

• On observing the scores we can score, there is only one possible odd number score that is 9.
• Therefore, to obtain 14 that is even score in 5 shots we have to add only even numbers or even number of odd numbers.
• But adding two odd numbers, $9+9$ gives 18 which exceeds required score of 14 points.
• Therefore, we have to obtain the score 14 only from 0,2,4 scores.
• only choosing 2's we can meet the requirement as we need 7 chances.
• choosing one 4 we can get again as we need 6 chances
• choosing two 4's, we need three 2's.------(1)
• choosing Three 4's, we need one 2.-------(2)
• these are the only two possibilities.
• Therefore, (1) can be scored by Two 4's, Three 2's in ⁵C₂= 10 ways
• (2) can be scored by three 4's, one 2 and one 0 in ⁵C₃*²C₁=20 ways.
• therefore, totally we can score 14 in 5 shots in 30 ways.