InterviewSolution
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InterviewSolution
| 1. |
The total number of injective mappings from a set with m elements to a set with n elements m ≤ n is equal to :(a) mn (b) nn(c) (n !/n-m) !(d) n ! |
| Answer» <p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif"><strong><span style="font-size:10pt">Correct option </span>n ! /(n -m) !</strong></span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif"><strong><span style="font-size:10pt">Explanation:</span></strong></span></span><span style="font-family:Arial,sans-serif; font-size:10pt"></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">Let A = {a<sub>1</sub>, a<sub>2</sub>, … am},B = {b<sub>1</sub>, b<sub>2</sub>, …, bn}, and let f : A → B. The possible choices for f (a<sub>1</sub>) are n.</span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">Having fixed f (a<sub>1</sub>), the possible choices for f (a<sub>2</sub>) are n − 1, and so on. Thus, there are</span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">n (n − 1) (n − 2) … (n − (m − 1)) = n !/(n -m) !</span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">injective mappings from A to B.</span></span></p> | |