a man has 5 male and 4 female relatives .his wife has male and 5 female relative's.the number of ways in which they can invite 5 male and female relatives so that 5 of them are man's relatives and 5 of them are females relatives
Answers
Answer:
Step-by-step explanation:
The possible cases are:
Case I : A man invites (3 ladies) and woman invites (3 gentlemen)
4
C
3
4
C
3
=16
Case II : A man invites (2 ladies,1 gentleman) and woman invites (2 gentleman, 1 lady)
(
4
C
2
3
C
1
)(
3
C
1
4
C
2
)=324
Case III : A man invites (1 lady, 2 gentlemen) and woman invites (2 ladies, 1 gentleman)
⇒(
4
C
1
3
C
2
)(
3
C
2
4
C
1
)=144
Case IV : A man invites (3 gentlemen) and woman invites (3 ladies)
3
C
3
3
C
3
=1
Total number of ways
=16+324+144+1=485
Answer:
There are 4 possibilities
i) 3 ladies from husband's side and 3 gentleman from wife's side .
No. of ways in this case=
4
C
3
×
4
C
3
=4×4=16.
ii) 3 gentleman from husband's side and 3 ladies from wife's side.
No. of ways in this case=
3
C
3
×
3
C
3
=1×1=1
iii) Two ladies & one gentleman from husband's side and one lady and two gentleman from wife's side.
No. of ways in this case=(
4
C
2
×
3
C
1
)(
3
C
1
×
4
C
2
)=(3×6)
2
=324
iv) One lady and two gentlemen from husband's side and 2 ladies and one gentleman from wife's side.
No. of ways in this case=(
4
C
1
×
3
C
2
)×(
3
C
2
×
4
C
1