In how many ways we can assign five employees to 4 projects so th
| In how many ways we can assign five employees to 4 projects so that every employee is assigned to only one project and every project is assigned by at least one employee?
A. 240
B. 260
C. 300
D. 180
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
If A = m and B = n, then number of onto functions possible from A to B is
nm – nC1(n - 1)m + nC2(n-2)m – nC3(n-3)m+…………(-1)n-1 nCn-1(1)m
Explanation:
Here m = 5 and n = 4
Required number of ways = 45 – 4C1(3)5 + 4C2(2)5 – 4C3(1)5 + 0
= 1024 – 243 × 4 + 6 × 32 – 4
= 1024 – 972 + 192 – 4
= 240