Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A×B. Then:
A
y=273x
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B
2y=91x
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C
y=91x
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D
2y=273x
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Solution
The correct option is B2y=91x Given, n(A)=3,n(B)=5 ⇒n(A×B)=15
Number of one-one functions from A to B is x=5×4×3 ⇒x=60
Number of one-one function from A to A×B is y=15×14×13 ⇒y=15×4×144×13 ⇒y=60×72×13 ⇒2y=(13)(7x)⇒2y=91x