Question:
Mark the correct alternative in the following question:
If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is
(a) ${ }^{10} \mathrm{C}_{7}$
(b) ${ }^{10} \mathrm{C}_{7} \times 7 !$
(c) $7^{10}$
(d) $10^{7}$
Solution:
As, the number of one-one functions from $A$ to $B$ with $m$ and $n$ elements, respectively $={ }^{n} P_{m}={ }^{n} C_{m} \times m !$
So, the number of one-one functions from $A$ to $B$ with 7 and 10 elements, respectively $={ }^{10} P_{7}={ }^{10} C_{7} \times 7 !$
Hence, the correct alternative is option (b).
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