A group of professional comprises of three lawyers, two teachers and five accountants. A committee of four members is selected from these professional. Calculate the number of ways to form the committee if there are exactly two of the three professions
Answers
Answer:
option A is the correct answer
Given : A group of professional comprises of three lawyers, two teachers and five accountants.
A committee of four members is selected from these professional.
To Find: the number of ways to form the committee if there are exactly two of the three professions
Solution:
Lawyers = 3
Teachers = 2
Accountants = 5
Three cases : exactly two of the three professions
Lawyers + teacher , Lawyers + accountant , Teacher + Accountant
Lawyers + teacher = 5
4 out of 5 can be selected in ⁵C₄ = 5 ways
Lawyers + accountant = 8
4 out of 8 can be selected in ⁸C₄ = 70 ways
Teacher + Accountant = 7
4 out of 7 can be selected in ⁷C₄ = 35 ways
Total Ways = 5 + 70 + 35 = 110
110 ways to form the committee if there are exactly two of the three professions
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