Question

In order to pass an examination, a minimum is to be secured in each of the 7 subjects. In how many ways can a student fail?

Answer 1

Answer:

127

Step-by-step explanation:

Hi,

Given that for a student to pass an examination , a minimum has to be

secured in each of the 7 subjects.

A student would fail if he doesn't secure a minimum in any one of

the subjects A student would fail either if he fails in 1 subject or he fails

in 2 subjects or 3 subjects or so on continuing.........or fails in all the

subjects

A student can fail in 1 subject in ⁷C₁ ways

A student can fail in 2 subjects in ⁷C₂ ways

A student can fail in 3 subjects in ⁷C₃ ways

......

.....

A student can fail in all subjects in ⁷C₇ = 1 way

So, total number of ways in which student would fail an examination are

(⁷C₁ + ⁷C₂ + .......+ ⁷C₇) = 2⁷ - 1 = 127

Hope, it helps !