Permutation and Combination MCQs

In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?

In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?

A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.

A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed?

How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?

How many arrangements of four 0's (zeroes), two 1's and two 2's are there in which the first 1 occur before the first 2?

How many different five-letter words can be formed using the letter from the world APPLE?

I have an amount of Rs. 10 lakh, which I went to invest in stocks of some companies. I always invest only amounts that are multiples of Rs 1 lakh in the stock of any company. If I can choose from among the stocks of five different companies, In how many ways can I invest the entire amount that I have?