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Mathematics
Mathematics
Problem
Let
A
=
{
x
1
,
x
2
,
x
3
,
x
4
,
x
5
,
x
6
,
x
7
}
A = \{x_1, x_2, x_3, x_4, x_5, x_6, x_7\}
A
=
{
x
1
,
x
2
,
x
3
,
x
4
,
x
5
,
x
6
,
x
7
}
and
B
=
{
y
1
,
y
2
,
y
3
}
B = \{y_1, y_2, y_3\}
B
=
{
y
1
,
y
2
,
y
3
}
. The total number of functions
f
:
A
→
B
f: A \to B
f
:
A
→
B
that are onto and there are exactly three elements
x
x
x
in
A
A
A
such that
f
(
x
)
=
y
1
f(x) = y_1
f
(
x
)
=
y
1
is equal to (a)
12
×
7
C
3
12 \times {}^7C_3
12
×
7
C
3
(b)
15
×
7
C
3
15 \times {}^7C_3
15
×
7
C
3
(c)
16
×
7
C
3
16 \times {}^7C_3
16
×
7
C
3
(d)
14
×
7
C
3
14 \times {}^7C_3
14
×
7
C
3
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