9 students of class 12 text th of whom 2 from section A, 3 from section B and 4 from section C are available for inter school debate competition. Number of ways in which 4 students can be selected so that there is atleast 1 from each section, is

Question

9 students of class 12 text th of whom 2 from section A, 3 from section B and 4 from section C are available for inter school debate competition. Number of ways in which 4 students can be selected so that there is atleast 1 from each section, is (A) 144 (B) 120 (C) 72 (D) 71

Tardigrade Admin · Accepted Answer

Hence 2 C 1 ⋅ 3 C 1 ⋅ 4 C 2+ 2 C 1 ⋅ 3 C 2 ⋅ 4 C 1+ 2 C 2 ⋅ 3 C 1 ⋅ 4 C 1 =36+24+12=72

Q. 9 students of class $1 2^{th}$ of whom 2 from section A, 3 from section B and 4 from section C are available for inter school debate competition. Number of ways in which 4 students can be selected so that there is atleast 1 from each section, is

144

120

72

71

Hence $^{2} C_{1} \cdot^{3} C_{1} \cdot^{4} C_{2} +^{2} C_{1} \cdot^{3} C_{2} \cdot^{4} C_{1} +^{2} C_{2} \cdot^{3} C_{1} \cdot^{4} C_{1}$
$= 36 + 24 + 12 = 72$

Q. 9 students of class 12th of whom 2 from section A, 3 from section B and 4 from section C are available for inter school debate competition. Number of ways in which 4 students can be selected so that there is atleast 1 from each section, is

144

120

72

71

Hence 2C1​⋅3C1​⋅4C2​+2C1​⋅3C2​⋅4C1​+2C2​⋅3C1​⋅4C1​ =36+24+12=72

Q. 9 students of class $1 2^{th}$ of whom 2 from section A, 3 from section B and 4 from section C are available for inter school debate competition. Number of ways in which 4 students can be selected so that there is atleast 1 from each section, is

Hence $^{2} C_{1} \cdot^{3} C_{1} \cdot^{4} C_{2} +^{2} C_{1} \cdot^{3} C_{2} \cdot^{4} C_{1} +^{2} C_{2} \cdot^{3} C_{1} \cdot^{4} C_{1}$
$= 36 + 24 + 12 = 72$