Question

The number of functions f from the set $A=$ {0, 1, 2} to the set $B=$ {0, 1, 2,3, 4, 5, 6, 7} such that $f\left(i\right)\le f\left(j\right)$ for $i<j$ and $i,j\in A$ is

• A. ${}^8{C}_3$
• B. ${}^8{C}_3$ + 2(${}^8{C}_2$)
• C. ${}^1{}^0{C}_3$
• D. ${}^9{C}_3$

Answer 1

Answer: (C)

${}^1{}^0{C}_3$

No. of ways $=$ No. of $1-1$ mappings $+$ No. of mappings in which 0 and 1 maps to same element and 2 maps different element $+$ 0 maps to different element and 1 and 2 maps to same element $+$ no. of constant functions
${=}^8{C}_3{+}^8{C}_2{+}^8{C}_2{+}^8{C}_1{=}^{10}{C}_3$