Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If α is the number of one-one functions from X to Y and β is the number of onto functions from Y to X, then the value of 1/5!(β−α) is
Answers
Answered by
0
Answer:
n(X)=5
n(Y)=7
⇒α→ Number of one-one function =
7
C
5
×5!
⇒β→ Number of onto function Y to X
1,1,1,1,3 1,1,1,2,2
⇒
3!4!
7!
×5!+
(2!)
3
3!
7!
×5!=(
7
C
3
+3.
7
C
3
)5!=4×
7
C
3
×5!
⇒
5!
β−α
=4×
7
C
3
−
7
C
5
=4×35−21=119.
Similar questions