GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 10

Question

Let $S_1 = \{1,2,3,\ldots,100\}$ and $S_2 = \{a,b,c,\ldots,z\}.$ Number of one-one (injective) functions from $S_2 \to S_1$ when $f(m) = 13$ is $\_\_\_$

• A. $^{100}P_{25}$
• B. $^{99}C_{25}$
• C. $^{99}P_{25}$
• D. $1$

Answer 1

Since, $m$ is already mapped, we are left with $25$ elements in the domain set and $99$ elements (since function is one-one we cannot map to an already mapped element). Number of possible into functions is nothing but choosing $25$ elements from $99$ where the order matters (order specifies the mapping of each of the $25$ elements in the domain set). This is given by
$^{99}P_{25}$

Comments

what does f(m)=13 shows?

---

Its mean M is mapped with 13.