Let the range of the function f: 1,2,3,4,5 arrow 1,2,3,4,5 assumes exactly 3 distinct values. If the number of such function is N, then find the value of ( N /300).

Question

Let the range of the function f: 1,2,3,4,5 arrow 1,2,3,4,5 assumes exactly 3 distinct values. If the number of such function is N, then find the value of ( N /300). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Since range contains exactly 3 distinct values <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/dc54e54a1f653fd13d0768ae83e2dcab-.png" /> ∴ 5 C 3[(5 !/1 ! 1 ! 3 !) (1/2 !)+(5 !/1 ! 2 ! 2 !) (1/2 !)] × 3 !=1500 . So, ( N /300)=(1500/300)=5.

Q. Let the range of the function $f : {1, 2, 3, 4, 5} \to {1, 2, 3, 4, 5}$ assumes exactly 3 distinct values. If the number of such function is $N$ , then find the value of $\frac{N}{300}$ .

Since range contains exactly 3 distinct values

$∴^{5} C_{3} [\frac{5 !}{1 ! 1 ! 3 !} \frac{1}{2 !} + \frac{5 !}{1 ! 2 ! 2 !} \frac{1}{2 !}] \times 3! = 1500.$
So, $\frac{N}{300} = \frac{1500}{300} = 5$ .

Q. Let the range of the function f:{1,2,3,4,5}→{1,2,3,4,5} assumes exactly 3 distinct values. If the number of such function is N, then find the value of 300N​.

Since range contains exactly 3 distinct values ∴5C3​[1!1!3!5!​2!1​+1!2!2!5!​2!1​]×3!=1500. So, 300N​=3001500​=5.

Q. Let the range of the function $f : {1, 2, 3, 4, 5} \to {1, 2, 3, 4, 5}$ assumes exactly 3 distinct values. If the number of such function is $N$ , then find the value of $\frac{N}{300}$ .

Since range contains exactly 3 distinct values

$∴^{5} C_{3} [\frac{5 !}{1 ! 1 ! 3 !} \frac{1}{2 !} + \frac{5 !}{1 ! 2 ! 2 !} \frac{1}{2 !}] \times 3! = 1500.$
So, $\frac{N}{300} = \frac{1500}{300} = 5$ .