Question -
Answer -
Given:
Total number ofofficers = 4
Total number of jawans= 8
Total number ofselection to be made is 6
(i) to include exactly oneofficer
Number of ways = (no.of ways of choosing 1 officer from 4 officers) × (no. of ways of choosing 5jawans from 8 jawans)
= (4C1)× (8C5)
By using the formula,
nCr = n!/r!(n – r)!
(ii) to include at leastone officer?
Number of ways =(total no. of ways of choosing 6 persons from all 12 persons) – (no. of ways ofchoosing 6 persons without any officer)
= 12C6 – 8C6
By using the formula,
nCr = n!/r!(n – r)!
= (11×2×3×2×7) – (4×7)
= 924 – 28
= 896 ways
∴ The required no.of ways are 224 and 896.