A committee is to be formed in a college. Committee consists of 2 prof

1.	A committee is to be formed in a college. Committee consists of 2 professors and 2 students. If there are 10 professors and 20 students. Find the number of ways to form a committee.1. 85502. 25503. 90504. 80555. 3550
Answer» Correct Answer - Option 1 : 8550 Given: Total number of professors = 10 Total number of students = 20 Committee consists of 2 professors and 2 students Number of ways to form a committee Formula used: ⁿC_r = n!/ [r! (n – r)!] Calculation: Select 2 committee members from professors and 2 committee members from students. ⇒ ¹⁰C₂× ²⁰C₂ = [(10!)/(2! × 8!)] [(20!)/ ( 2! × 18!)] ⇒ [(10 × 9 × 8!)/ (2! × 8!)] [(20 × 19 × 18!)/ 2! × 18!] ⇒ 45 × 190 ⇒ 8550 ways ∴ Total number of ways to form a committee is 8550

A committee is to be formed in a college. Committee consists of 2 professors and 2 students. If there are 10 professors and 20 students. Find the number of ways to form a committee.1. 85502. 25503. 90504. 80555. 3550

Answer» Correct Answer - Option 1 : 8550

Given:

Total number of professors = 10

Total number of students = 20

Committee consists of 2 professors and 2 students

Number of ways to form a committee

Formula used:

ⁿC_r = n!/ [r! (n – r)!]

Calculation:

Select 2 committee members from professors and 2 committee members from students.

⇒ ¹⁰C₂× ²⁰C₂ = [(10!)/(2! × 8!)] [(20!)/ ( 2! × 18!)]

⇒ [(10 × 9 × 8!)/ (2! × 8!)] [(20 × 19 × 18!)/ 2! × 18!]

⇒ 45 × 190

⇒ 8550 ways

∴ Total number of ways to form a committee is 8550

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