Question

a tech company there 15 programmer 7 designers and 11 salespeople. the company needs 12 volunteers to represent at upcoming conference.
how many ways are there to choose the 12 people given the following situations:
1. there are no restrictions?
2. there are an equal number from each group?
3. six programmers are chosen?
4. Mohamed must be included?
5. ryan must not be chosen?
6. Jessica and ryan cannot work together?
7. at least one designer is chosen?

Answer 1

(1) We have 15 - programmer 7- designers salespeople 11 Total = 15+7+11 = 33 -people if no restriction then 12-people can be choose in 33 C 354,817,320 12 (2) each group Equal Number from can be choose 4- from each group that is 15 Cux ncu x "Ca = 1365X 35 X 330 15,765,750 are there (3) sia programmer rest slu people it So from rest 18 be done in can 18 15 C6 Х C6 = 5005% 18,564 92,912,820

ų So 11 we Mohamed must need from rest done in be included to choose it 32 can be 32 cu 129,024,480 ll 5 Ryan not 12 people from 32 included So all which is 32 C 12 225,792840 6 or or none 31612 Either Jessica ryan of both choosen 32 32 31 Clat Cig = a (3&Cia) + 12 12 = 451,585,680 +141,120,525 = 592,7069205 Atleast degigner means No designer 7 one - Total 33C 26 C12 12 – 354,817,820–9,657,700 = 345,159,620