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

Options

  1. A150
  2. B144
  3. C147
  4. D154

Correct answer

A. 150

Step-by-step solution

Total number of functions = 3 5 (since each of 1,2 , 3,4 or 5 can correspond to any of a , b or c ) The number of functions that corresponds to only one element of B is 3 C 1 × 1 5 and the number of functions that correspond to atmost two elements of B is 3 C 2 × 2 5 . Total number of onto functions = 3 5 - 3 C 2 × 2 5 + 3 C 1 × 1 5 = 243 - 96 + 3 = 150 3 C 1 × 1 5 i s r e p e a t e d t w i c e i n 3 C 2 × 2 5

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