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May 29, 2015

Homework Help: Discrete Math

Posted by Francesca on Tuesday, April 12, 2011 at 10:55am.

Is this correct?

Using the Principle of Inclusion-Exclusion, find the number of integers between 1 and 2000 (inclusive) that are divisible by at least one of 2, 3, 5, 7.

A = {n| 1 ≤ n ≤ 2000, 2 |n}
B = {n| 1 ≤ n ≤ 2000, 3 |n}
C = {n| 1 ≤ n ≤ 2000, 5 |n}
D = {n| 1 ≤ n ≤ 2000, 7 |n}

|A| = [2000/2] = 1000
|B| = [2000/3] = 666
|C| = [2000/5] = 400
|D| = [2000/7] = 285

Also, I'm kind of confused with how to approach this problem:

John Sununus was once the governor of New Hampshire, and his name reminds one of the authors of a palindrome (a words which is spelt the same way forwards as backwards, such as SUNUNUS).

How many seven-letter palindromes (not necessarily real words) begin with the letter S and contain at most three letter?

Thanks for any helpful replies!

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