0 votes 0 votes A and B are two sets. If |A| = 5 , |B| = 3 , then, the number of onto functions from A to B are ___ ? (A) 35 (B) 150 (C) 29 (D) 27 Mathematical Logic geeksforgeeks-test-series relations + – Sarvottam Patel asked Jan 13, 2017 Sarvottam Patel 416 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes By principle of inclusion-exclusion: 35 - [$\binom{3}{1}*2^{5} - \binom{3}{2}*1^{5}$] = 150 Sushant Gokhale answered Jan 13, 2017 Sushant Gokhale comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes Sushant's answer is correct, you can take a generalized way if set A has cardinality m (here 5) and set B has cardinality n (here 3 ) , the number of onto functions are = (nC0) nm - (nC1) .(n-1)m + (nC2) .(n-2)m - ... + (-1)n (nCn-1) .(1)m = 35 - (3C1)∗25 + (3C2)∗15 = 150 pps121 answered Jan 14, 2017 pps121 comment Share Follow See all 0 reply Please log in or register to add a comment.