Question

Number of words formed using all of a,e,e,g,r such that a is adjacent to an e:

• 60
• 48
• 42
• 24

Solution

Let A be the set of all words such that ea occurs together. So we need to arrage, ea,e,g,r

The number of elements in this set are =4! =24

Let B be the set of all words such that ae occurs together. So we need to arrage, ae,e,g,r

The number of elements in this set are =4! =24

So we should just add the two? No, there are some cases which are counted in both. These are the cases where eae occurs.

So the number of such cases is =3! =6

So the number of favorable cases =24+24-6=42