Permutation & Combination Level-3 Quiz-2

1. From a box containing n items, if at most (n – 2) items can be selected in 247 ways, find the number of ways of selecting at least 3 item.

2. Five boys including Suresh and five girls including Suneeta are to be seated around a circular table such that no two boys are adjacent and Suneeta is not adjacent to Suresh. In how many ways can this be done?

3. How many multiples of 4 greater than 40,000 but less than 70,000 can be formed using the digits 0, 1, 3, 4, 6, 7, 8, if repetition of digits is allowed?

4. From a collection of umbrellas hung in a row, one or more can be selected in 511 ways. In how many ways can 4 umbrellas be selected such that the selection contains no two consecutive umbrellas?

5. In a convex polygon with n sides, the number of points of intersection of the diagonals in the interior of the polygon is 70. Find the minimum value of n?

6. The letters of the word BANANA are permuted in all possible ways and listed in alphabetical order as in a dictionary. What is the rank of the word NANAAB?

7. In how many ways is it possible to choose a white square and a black square on a chess board so that the squares must not lie in the same row or column?

8. Suppose n is an integer such that the sum of the digits of n is 2, and 10^10 < n < 10^11. Find the number of different values for n?

9. ABC is a three-digit number in which A > 0. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B?

10. N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?