How many $7$-letter sequences are there with at least six different letters? exactly five different letters?

Question

How many $7$- letter sequences are there if:

(1.) there are at least $6$ different letters

(2.) exactly $5$ different letters

( out of $7$ positions for both as mentioned above)

what should be my approach?

Answer 1

HINT:

1) For "at least" and "no more than" statements it is a good approach to subtract the undesired ones (the complement set so to say) from all possible combinations

2) In this case you will have $2$ similar characters, look up permutations of a multiset

PS: Try to add as much context to your question as possible i.e. what you have tried, where are you stuck, what alphabet are we using here for this particular question. We are here to learn, educate and share ideas and the community will receive questions without an effort in a bad way.

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Edit:

@jl00 may have a point in the comments

There are $2$ cases

• $6$ different letters
• $7$ different letters

For case one: you will need to figure out in how many ways you can choose these $6$ letters. One of them will be repeated, in how many ways can you choose this repeated one? How many ways can you arrange these letters?