# (Combinatorics) A bicycle manufacturer decided to offer electric bicycles to university students.

35 students got a red colored bicycle and another 10 students got a green colored bicycle. Another 15 students changed their mind and decided not to accept

## 1 Answer

You are right. There is a toal of 60 students. You first choose 35 students who get a red bicycle, then choose 10 students who get a green bicycle, and then the remaining 15 students will get no bicycle in ${15\choose 15}=1$ ways. So the number of different ways is going to be

$${60\choose 35}{25\choose 10}{15\choose 15}.$$

You can do this in any order, the number of different ways is also equal to

$${60\choose 10}{50\choose 35}{15\choose 15}.$$

This means you first chose the 10 students who get no bicycle, the choose students who get a red bicycle, and then the ones who get a green bicycle.

Or

$${60\choose 15}{45\choose 35}{10\choose 10}.$$

You can check that all this formulas give you the same number.

- 1 Answer
- 107 views
- Pro Bono

### Related Questions

- Logic quesiton A v ¬A
- Discrete math- Range and preimage of the floor function
- Discrete Math/ Set theory Question
- Discrete math
- Logic Question 𝐴∧(𝐵∨𝐶)⊢(𝐴∧𝐵)∨(𝐴∧𝐶)
- Logic Question (𝐴→(𝐵→𝐶))→((𝐴→𝐵)→(𝐴→𝐶))
- Singular Value Decomposition Example
- Count the number of decks of cards, where no king is on top of the ace of the same suit.