A mar has 10 freinds among whom two are married to each other. she wishesh to invite 5 of them for a party. if the married couple refusses to attend seperately then the number of different ways in which she can invite five freinds is
Permutation and combination
As we can see 8 are unmarried people, and 2 are married to each other, and since the married couple refuses to attend seperately, the total invitations are 9.
If the couple is excluded she has to select 5 people from 8, so 8C5.
If the couple is included she has to select 3 people from 8, so 8C3.
Hence the total number of ways = 8C5 + 8C3 = 56 + 56 = 112.