Permutations and Combinations

How many 3-digit numbers are there whose digits are all prime numbers?

• 125

• 64

• 81

• 243

• None of these.

We roll a die five times and write down the numbers we get in the order we get them, thus we obtain a 5-digit number. How many different numbers can be obtained in this way?

• 117649 numbers

• 720 numbers

• 7776 numbers

• 120 numbers

• None of these.

Decide which statement(s) is (are) true for the following problem:

We insert 7 coins in a parking meter. There are 3 identical coins among them. In how many ways can we insert the seven coins if only one can be inserted at a time?

• order matters

• the number of elements is equal to the number of places

• repetition is not allowed

• The answer is: 840.

• The answer is: 35.

Decide which of the statement(s) is (are) true for this problem:

In how many ways can you fill in a lottery ticket if you have to mark 5 numbers out of 90?

• order matters

• the number of elements is equal to the number of places

• repetition is not allowed

• The answer is greater than 40 million.

• The answer is greater than 400 million.

In how many ways can you fill in a lottery ticket if you have to mark 6 numbers out of 45 ?

• 8,145,060 ways

• 720 ways

• 5,864,443,200 ways

• 8,303,765,625 ways

• None of these

In a poetry-telling competition 4 boys and 6 girls performed excellenty. For a school celebration 3 boys and 3 girls need to be chosen from them. In how many ways can we do so?

• 210 ways

• 36 ways

• 17280 ways

• 80 ways

• None of these

A family of six members won two tickets to the theatre in a tombola. In how many ways can they choose who will go?

• 30 ways

• 15 ways

• 36 ways

• 360 ways

• None of these

In a class of 29 there are 14 girls. The class would like to put a play on stage in which there are 10 characters, 4 of whom are female. In how many ways can they set up the cast?

• 20,030,010 ways

• 5,010,005 ways

• 6.5973*10^18 ways

• 210 ways

• None of these.

There have been 8 questions in this quiz so far. In how many ways could these questions be rearranged?

• 40,320 ways

• 20,160 ways

• 16,777,216 ways

• 5040 ways

• None of these.

How difficult were the questions in this quiz?

• Very difficult.

• Quite difficult.

• Not really difficult.

• Very easy.