Combinatorics

9000139704

Level: 
C
There are \(5\) different kinds of cakes in a shop. Find the number of possibilities how to buy \(8\) cakes in this shop. (There is more than \(8\) cakes of each kind available.)
\(\frac{12!} {8!\, 4!}=495\)
\(5!\, 8!=4\:838\:400\)
\(5^{8}=390\:625\)
\(\frac{8!} {5!\, 3!}=56\)

9000139710

Level: 
C
The wallet contains nine coins: three \(1\)-Euro coins, three \(2\)-Euro coins and three \(5\)-Euro coins. How many different amounts can be paid if we have to pay the amount exactly and use just three coins for this payment?
\(\frac{5!} {3!\, 2!}=10\)
\(\frac{5!} {3!}=20\)
\(3^{3}=27\)
\(3!=6\)

9000153901

Level: 
C
Find the number of ways how to distribute \(8\) identical balls among \(5\) persons so that each of them gets at least one ball.
\(\left({7\above 0.0pt 3}\right) = 35\)
\(5^{3} = 125\)
\(\left({12\above 0.0pt 5} \right) = 792\)
\(\left({12\above 0.0pt 8} \right) = 495\)

9000153906

Level: 
C
Find the number of ways how to distribute \(5\) identical balls among \(8\) persons so that no persons gets more than one ball.
\(\frac{8!} {5!3!} = 56\)
\(\frac{8!} {3!} = 6\:720\)
\(\left({12\above 0.0pt 8} \right) = 495\)
\(\left({12\above 0.0pt 5} \right) = 792\)