Question

If P = {1, 2, 3, 4, 5} and Q = {a, b, c}, then number of onto function from P to Q is

• A. 150
• B. 144
• C. 147
• D. None of these

Answer 1

Answer: (A)

150

Answer 2

Number of total functions

= 3⁵ (since each of 1, 2, 3, 4 or 5 can correspond to any of a, b or c)

Number of function that correspond to only one element of B = $3C_{1}x1^{5}$ and, number of functions which correspond to two or less element of B = $3C_{2}x2^{5}$.

∴ Total “onto” function = 3⁵ - $3C_{2}x2^{5} +^{3}C_{1}x1^{5}$

=243 – 96 + 3 = 150

$(^{3}C_{1}x1^{5}$ is repeated twice in ).