Question 2

Hi Emma. Have you studied permutations?

Using four cards, we can form a number greater than 4000 by placing 4, 5 or 6 in the first slot and then placing three of the remaining four digits in the other slots.

A few examples (starting with 4): 4235, 4325, 4523, 4632, 4256, 4365

How many different ways can we order three digits out of the set of remaining digits: {2,3,5,6}?

The topic of permutations tells us there are 24 ways. We could get 24 by drawing a tree diagram, using a counting rule or applying a formula.

Next, follow the same logic when the four-digit number starts with 5, instead of 4. And again, when it starts with 6. Add up all of the ways.

Please tell us what you've seen before. If you haven't yet learned this type of counting, be sure to let us know. (We can help you find links to online lessons.)

Edited: Forgot to mention numbers starting with 5 and 6. (Thank you, Subhotosh.)

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Since you want numbers >4000, you should also consider placing other numbers at the "first slot".

There are other - but somewhat similar - ways to do this problem.
 
If you use all 5 cards will the number always be greater than 4000? If, yes then how many ways can you arrive these five cards?

What do you do with the number of 4 cards combinations with the number of 5 cards combinations to get your answer?
 
Jomo said:
… do with the number of 4 cards combinations with the number of 5 cards combinations …
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With with? :p

By the way, those are 'permutations', as in: "the number of 4-card permutations and the number of 5-card permutations".

\(\;\)
 
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