Combinations

[true meadow]

I'm confused on how to approach this problem:
"Find the number of length-7 sequences (so order matters) from the numerical digits {0,1,2,3,4,5,6,7,8,9} such that the sequence uses exactly 4 different digits."
Any help on how to solve this problem would be appreciated please.

[frigid glacier]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations

[winter lynx]

9C4 × 4⁷

Exactly a type of question I expect from a Pranav

[true meadow]

I don't get it how?

[winter lynx]

Wait that will be 10C4, the number of ways to choose 4 out of 10 numbers in the set

Then the sequence can be found in 4⁷ ways

[misty fulcrum]

This is

• The number of ways you can pick 4 distinct digits from that set of 10
  times
• The number of distinct length-7 sequences you can make out of those four digits.

it's already been said, but do you understand how you'd calculate each of these values?

[winter lynx]

Unfortunately he is lost, there won't be a response in this regard

[misty fulcrum]

"lost"?

[winter lynx]

Yeah, we lost him.

[true meadow]

yea thanks for breaking it down. This makes sense but I'm quite sure how to approach this

[jovial flax]

@true meadow has given 1 rep to @misty fulcrum

[true meadow]

how is it 4^7?

[true meadow]

would it be something like 10C4 * 7P4?

[winter lynx]

Nope

By seven length sequence

If we have 7 spaces and we can fill each space by any one of the 4 numbers we will get
4c1 × 4c1 ×... × 4c1 = 4×4×...×4 = 4⁷ ways