1. Ramesh has 6 friends. In how many ways can he invite one or more of them at dinner ?

- Option : C
- Explanation :
Total number of possibilities,

If he calls one friend: 6 ways

If he calls two friends: 6C2

If he calls three friends: 6C3

Similarly solving up to the case where he can call all the 6 friends...

Total number of cases will be 63

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2. The number of ways to arrange the letters of the word CHEESE are

- Option : A
- Explanation : The total number of ways to arrange a word with n letters is n!
But since here the letter E repeats 3 times we will divide 6! by 3!.

Hence answer will be 120

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- Option : A
- Explanation : The president can be Plected in twenty-six different ways; following this, the treasurer can he elected in twenty-five different ways (since the person chosen president is :-:ot eligible to be treasurer); and following this, the secretary can be elected in twenty-four different ways. Thus, by above principle of counting, there are n = 26 x 25 x 24 = 15 600 different ways in which the organization can elect the officers.

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Common Data for next 2 questions

There are four bus lines between A and B; and three bus lines between B and C.

5. The number of ways a person can travel by bus from A to C by way of B will be

- Option : B
- Explanation : There are four ways to go from A to B and three ways to go from B to C. Hence there are 4 x 3 = 12 ways to go from A to C by way of B.

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