Number of ways in which three distinct numbers can be chosen from the set 1,2,3,4,5,6,7,8,9,10 such that a

Question

Number of ways in which three distinct numbers can be chosen from the set 1,2,3,4,5,6,7,8,9,10 such that a < b < c and c - b = b - a, is (A) 10 (B) 20 (C) 30 (D) none

Tardigrade Admin · Accepted Answer

S 1= 1,3,5,7,9 S 2= 2,4,6,8,10 ∴ 5 C 2+ 5 C 2=20

Q. Number of ways in which three distinct numbers can be chosen from the set ${1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$ such that $a < b < c$ and $c - b = b - a$ , is

10

20

30

none

$S_{1} = {1, 3, 5, 7, 9}$
$S_{2} = {2, 4, 6, 8, 10}$
$∴^{5} C_{2} +^{5} C_{2} = 20$

Q. Number of ways in which three distinct numbers can be chosen from the set {1,2,3,4,5,6,7,8,9,10} such that a<b<c and c−b=b−a, is

10

20

30

none

S1​={1,3,5,7,9} S2​={2,4,6,8,10} ∴5C2​+5C2​=20

Q. Number of ways in which three distinct numbers can be chosen from the set ${1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$ such that $a < b < c$ and $c - b = b - a$ , is

$S_{1} = {1, 3, 5, 7, 9}$
$S_{2} = {2, 4, 6, 8, 10}$
$∴^{5} C_{2} +^{5} C_{2} = 20$