Concept:The number of ways to select a group from two different categories is found by multiplying combinations from each category, and then adding the cases that satisfy the condition (at least one typist).
Explanation:We have 6 programmers and 4 typists, total 10 people.
We need to choose 5 people with at least one typist.
We consider four separate cases based on the number of typists in the group.
Case 1: 1 typist, 4 programmersChoose 1 typist from 4:
C(4,1)=4 ways.
Choose 4 programmers from 6:
C(6,4)=15 ways.
Total for this case:
4×15=60 ways.
Case 2: 2 typists, 3 programmersChoose 2 typists from 4:
C(4,2)=6 ways.
Choose 3 programmers from 6:
C(6,3)=20 ways.
Total:
6×20=120 ways.
Case 3: 3 typists, 2 programmersChoose 3 typists from 4:
C(4,3)=4 ways.
Choose 2 programmers from 6:
C(6,2)=15 ways.
Total:
4×15=60 ways.
Case 4: 4 typists, 1 programmerChoose 4 typists from 4:
C(4,4)=1 way.
Choose 1 programmer from 6:
C(6,1)=6 ways.
Total:
1×6=6 ways.
Add all cases:
60+120+60+6=246 total ways.
Answer:246 ways (Option C).