Test Preparation on Mathematics-Permutation and Combination

1.

The least positive integer n for which _{n-1}C_{5}+_{n-1}C_{6} < _{n}C_{7} is _______

2.

n books are arranged on a shelf so that two particular books are not next to each other, There were 480 arrangements altogether. Then the number of books on the shelf is ________

3.

The sum of all possible numbers greater than 10000 formed by using the digits from { 1,3,5,7,9} is

4.

How many words can be formed by taking four different letters of the word MATHEMATICS ?

5.

6.

If ^{n}C_{r} = ^{n}C_{r-1} and ^{n}P_{r} = ^{n}P_{r + 1} , then the value of n is

7.

How many different nine digit numbers can be formed from the number 22,33,55,888 by rearranging its digits so that the odd digits occupy even positions ?

8.

The number of arrangements that can be made out of the letter of the word " SUCCESS " so that the all S's do not come together is

9.

If the coefficient of the 5th, 6th and 7th terms of the expansion of (1+x)^{n}are in A.P then the value of n may be _______

10.

The number of numbers greater than 3000, which can be formed by using the digits 0,1,2,3,4,5 without repetition is _______