1. To calculate the number of combinations for n distinguishable items:
Three laboratories to be cleaned: Biosorption, Pilot Plant and Fermentation. How many different combinations of cleaning the three laboratories? n=3, r=2
1st
2nd
Not done B P F B F P P B F P F B
3 different combinations F B P F P B

2. To calculate the number of permutations for n distinguishable items:
Three laboratories to be cleaned: Biosorption, Pilot Plant and Fermentation. How many different sequences of cleaning the three laboratories? n=3, r=2
1st
2nd
Not done B P F B F P P B F P F B
6 different sequences F B P F P B

3. } } } To calculate the number of permutations with classes:
There are three blocks to be ranged and two (No.#2 and No#3) of them are the same. How many orders can the three blacks be arranged? n=3, r=3, n1=1, n2=2 1 2 3 }
same, 1st arrangement 1 3 2 2 1 3 }
2nd arrangement 3 1 2 2 3 1 }
3rd arrangement 3 2 1