Question

The total number of function ‘ƒ’ from the set {1, 2, 3} into the set {1, 2, 3, 4, 5} such that ƒ(i) £ ƒ(j), " i < j, is equal to-

• A. 35
• B. 30
• C. 50
• D. 60

Answer 1

Answer: (A)

35

Answer 2

Let ‘l’ is associated with ‘r’ ,

r Ī {1, 2, 3, 4, 5} then ‘2’ can be associated with r, r + 1, ….., 5.

Let ‘2’ is associated with ‘j’ then 3 can be associated with j, j + 1, …., 5. Thus required number of functions

= $\sum_{r = 1}^{5}\left( \sum_{j = r}^{5}{(6 - j)} \right)$= $\sum_{r = 1}^{5}\frac{(6 - r)(7 - r)}{2}$

= $\frac{1}{2}$ $\left( \sum_{r = 1}^{5}{(42 - 13r + r^{2})} \right)$

= $\frac{1}{2}$ $\left( 42.5 - 13.\frac{6.5}{2} + \frac{5.6.11}{6} \right)$= 35

Hence (1) is correct answer.