Permutations an...

The number of arrangements of n different things taken r at a time which include a particular thing is

The number of arrangements of n different things taken r at a time which exclude a particular thing is

5 persons board a lift on the ground floor of an 8 storey building. In how many ways can they leave the lift?

If ¹²C₄ + ¹²C₅ =ⁿC₅  ,then n is equal to

A fair dice is rolled n times. The number of all the possible outcomes is

4 boys and 4 girls are to be seated in a row. The number of ways in which this can be done, if the boys and girls sit alternately, is

The letters of the word ‘SOCIETY’ are arranged in such a manner that the vowels and consonants occur alternately, the number of different words so obtained is

There are 10 true-false questions. The number of ways in which they can be answered is