Answer:
84 ways
Step-by-step explanation:
Given
Total individuals = 9
Available roles = 5
Required
Number of ways roles can be assigned.
First, it'll be assumed that no two individual shares a role and no single individual takes two roles.
Having said this, the number of ways the roles can be assigned can be calculated using the combination formula; as follows.
ⁿCr = C(n,r)
Where n represents the total individuals
n = 9
r represents the available roles
r = 5
So,
ⁿCr = C(n,r) =>
⁹C₆ = C(9,6)
⁹C₆= 9!/((9-6)!6!)
⁹C₆ = 9!/(3!6!)
⁹C₆ = (9 * 8 * 7 * 6!)/(6! * 3 * 2 * 1)
⁹C₆ = (9 * 8 * 7)/(3 * 2 * 1)
⁹C₆ = 504/6
⁹C₆ = 84
Hence, 9 roles can be assigned to 5 people in 84 ways
