Assignment -1
Grade Class 12
Question:
<p>If A and B have 4 and 6 elements respectively then the number of one-one function from A to B is</p>
<p style="display:inline">360</p>
<p style="display:inline">4<sup>6</sup></p>
<p style="display:inline">240</p>
<p style="display:inline">6<sup>4</sup></p>
Step-by-Step Solution
Key Concept: The number of one-one functions from set A to set B is determined by the number of permutations of n(B) elements taken n(A) at a time, denoted as ^{n(B)}P_{n(A)}.
<p>Giiven: n(A) = 4 and n(B) = 6.<br />
Since n(B) > n(A) and he function is one-one function.<br />
Thus, the number of one-one functions mapping from A to B is<br />
<span class="math-tex">\({ }^{n(B)} P_{n(A)}={ }^6 P_4\)</span><br />
= <span class="math-tex">\(\frac{6 !}{(6-4) !}\)</span> ...<span class="math-tex">\(\left[\because{ }^n P_r=\frac{n !}{(n-r) !}\right]\)</span><br />
= <span class="math-tex">\(\frac{6 \times 5 \times 4 \times 3 \times 2 !}{2 !}\)</span><br />
= 360</p>
Correct Answer: A