Given six line segments of length `2,3,4,5,6,7` units, the number of triangles that can be formed by these segments is -

Options

A. `.^(6)C_(3)-7`
B. `.^(6)C_(3)-6`
C. `.^(6)C_(3)-5`
D. `.^(6)C_(3)-4`

Answer

A

Explanation

for a `Delta` we have required three line segement and sum of two line segement must be gerater then `3^(rd)`
`= .^(6)C_(3) - 7`
`{(2,3,5)(2,3,6)(2,3,7)(2,4,6)(2,4,7)(2,5,7)(3,4,7)}`