Md.RakibulHasan
Susan invited 13 of her friends for her birthday party and created return gift hampers comprising one each of $3, $4, and $5 gift certificates. One of her friends did not turn up and Susan decided to rework her gift hampers such that each of the 12 friends who turned up got $13 worth gift certificates. How many gift hampers did not contain $5 gift certificates in the new configuration?
3 sets
we have 3,4,5 for 13 people which is redistributed among 12 ppl (so now sum for each person is 13). We can make this by 5 5 3; 4 4 5; 3 3 3 4. Now Qn asks to find how many sets dont have a 5 i.e. no of sets with 3334 combination. So far was the hard bit, now just solve (again dont manually solve as then the 2nd bit will be equally hard). Since you have 3334 we know the number of sets of these will have to be less than 5 (Why? coz total is 13 pieces available). Lets start with 4, means only 1 set of 553 will be possible wont work as we need to use up all 5’s. Try with 3, we get (5 5 3) *4 sets, (4 4 5)*5sets and (3 3 3 4)*3 sets. Total sets are 4+5+3=12 sets. Voila
Damn typing this took longer than solving it