Home
Class 12
MATHS
Find the number of all three elements su...

Find the number of all three elements subsets of the set`{a_1, a_2, a_3, a_n}` which contain `a_3dot`

Text Solution

Verified by Experts

The correct Answer is:
`.^(n-1) C_(2)`
The number of three elements subsets containing `a_(3)` is equal to the number of ways of selecting 2 elements out of n-1 elements. So, the required number of subsets is `.^(n-1)C_(2)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The number of all the possible triplets (a_1,a_2,a_3) such that a_1+a_2cos(2x)+a_3sin^2(x)=0 for all x is (a) 0 (b) 1 (c) 3 (d) infinite

Find the sum of first 24 terms of the A.P. a_1,a_2, a_3 ......., if it is inown that a_1+a_5+a_(10)+a_(15)+a_(20)+a_(24)=225.

A set contains (2n + 1) elements. The number of subsets of the which contain at most n elements is

Find the number of ways of arranging 15 students A_1,A_2,........A_15 in a row such that (i) A_2 , must be seated after A_1 and A_3 , must come after A_2 (ii) neither A_2 nor A_3 seated brfore A_1

Let A_r ,r=1,2,3, , be the points on the number line such that O A_1,O A_2,O A_3dot are in G P , where O is the origin, and the common ratio of the G P be a positive proper fraction. Let M , be the middle point of the line segment A_r A_(r+1.) Then the value of sum_(r=1)^ooO M_r is equal to (a) (O A_1(O S A_1-O A_2))/(2(O A_1+O A_2)) (b) (O A_1(O A_2+O A_1))/(2(O A_1-O A_2) (c) (O A_1)/(2(O A_1-O A_2)) (d) oo

The number of subsets of a set containing n distinct elements is

Determine the number of terms in a G.P., if a_1=3,a_n=96 ,a n dS_n=189.

The number of all possible triplets (a_1,a_2,a_3) such that : a_1 + a_2cos2x + a_3sin^2x = 0 for all x is :

If the area of the circle is A_1 and the area of the regular pentagon inscribed in the circle is A_2, then find the ratio (A_1)/(A_2)dot

Write the first three terms of the sequence defined by a_1= 2,a_(n+1)=(2a_n+3)/(a_n+2) .