2 n C3: n C2=44: 3 then value of n C3 is

Question

2 n C3: n C2=44: 3 then value of n C3 is (A) 20 (B) 35 (C) 56 (D) 10

Tardigrade Admin · Accepted Answer

( 2 n C 3/ n C 2)=(44/3) ⇒ 3 ⋅ 2 n C 3=44 ⋅ 2 C 2 ⇒ 3 ⋅ (2 n (2 n -1)(2 n-2)/3 !)=44 ⋅ ( n ( n -1)/2 !) ⇒ 4 n(n-1)(2 n-1)-44 n(n-1)=0 ⇒ 4 n(n-1)(2 n-1-11)=0 ⇒ n=6

Q. 2nC3​:nC2​=44:3 then value of nC3​ is

20

35

56

10

nC2​2nC3​​=344​⇒3⋅2nC3​=44⋅2C2​ ⇒3⋅3!2n(2n−1)(2n−2)​=44⋅2!n(n−1)​ ⇒4n(n−1)(2n−1)−44n(n−1)=0 ⇒4n(n−1)(2n−1−11)=0 ⇒n=6

Q. $^{2 n} C_{3} :^{n} C_{2} = 44 : 3$ then value of $^{n} C_{3}$ is