Discrete Math, URGENT please :(

I am stuck on these 2 questions I have absolutely NO CLUE I need help :( Its questions 2 and 3. Can anyone help me please

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Originally Posted by juliie

I am stuck on these 2 questions I have absolutely NO CLUE I need help :( Its questions 2 and 3. Can anyone help me please

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Please post the two questions. We cannot help with what cannot see.

sorry I didn't know how to use this at first I thought I posted the question anyway ill post the question now I hope you can help me!

Let m ≥ n and let A = {1,2,...,m} and let B = {1,2,...,n}. In this exercise you will determine a formula for the number of surjective functions from A to B. For each i ∈ B, let Ai denote the set of all functions f : A → B such that i is not in the image of f, that is, for all x ∈ A we have f(x) 6= i. Thus the set of all functions from A to B which are not surjective is
A1 ∪ A2 ∪ ··· ∪ An.

1. a) Let 1 ≤ k ≤ n. In how many ways can we choose integers i1,i2,...,ik such that 1 ≤ i1 < i2 < ··· < ik ≤ n?

b) Let 1 ≤ i1 < i2 < ··· < ik ≤ n. Show that |Ai1 ∩ Ai2∩ ··· ∩ Aik| = (n − k)^m.

Quote:

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Originally Posted by juliie

sorry I didn't know how to use this at first I thought I posted the question anyway ill post the question now I hope you can help me!

Let m ≥ n and let A = {1,2,...,m} and let B = {1,2,...,n}. In this exercise you will determine a formula for the number of surjective functions from A to B. For each i ∈ B, let Ai denote the set of all functions f : A → B such that i is not in the image of f, that is, for all x ∈ A we have f(x) 6= i. Thus the set of all functions from A to B which are not surjective is
A1 ∪ A2 ∪ ··· ∪ An.

1. a) Let 1 ≤ k ≤ n. In how many ways can we choose integers i1,i2,...,ik such that 1 ≤ i1 < i2 < ··· < ik ≤ n?

b) Let 1 ≤ i1 < i2 < ··· < ik ≤ n. Show that |Ai1 ∩ Ai2∩ ··· ∩ Aik| = (n − k)^m.

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NEVER, never post the same question more than once.