NIMCET 2008 Question Paper with solutions

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Question : 35 of 120

Marks: +1, -0

The number of functions

f

from the set

A=\{0,1,2\}

into the set

B=\{0,1,2,3,4,5,6,7\}

such that

f(i) ≤ f(j)

for

i < j

and

i, j ∈ A

is

$^{8} C_{2}$
$^{8} C_{3}+2( ^{8} C_{2})$
$^{10} {C}_{3}$
None of these

Solution:

For 0 , we have 8 options.
For

1,

number of options

=1+2+. . .+8

=\;{8 ⋅ 9}/{2}={ }^{9} C_{2}

For

2,

we have

∑↙{r=1}↖{8} \;{r(r+1)}/{2}

options

=\;{8 ⋅ 9 ⋅ 10}/{2 ⋅ 3}={ }^{10} C_{3}

options

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