SOLUTION: The following problems can be solved using the principle of inclusion-exclusion. Give the solutions by naming sets A1 , A2 , ... , Ak such that either the set or the complement

Question 1158215: The following problems can be solved using the principle of inclusion-exclusion. Give the solutions by
naming sets A1
, A2
, ... , Ak such that either the set or the complement of the set is counted by the
inclusion-exclusion formula.
(1) How many n-digit decimal sequences (using the digits 0 − 9) are there in which the digits 1, 2 and
3 all appear?
(2) How many ways are there of rolling a sided die 10 times in a sequence such that all 6 faces
appear?
(3) How many positive integers less than or equal to 420 are relatively prime to 420 ?
(hint: 420 = 2 )
2
· 3 · 5 · 7
(4) How many arrangements of 52 letters, 2 A’s, 2 B’s, 2 C’s, etc. with no pair of identical letters
exist?
(5) How many ways are there of dealing a 13 card hand with at least one void in a suit?
(6) How many 13 card hands have at least one picture card (i.e., J, Q, K, A)?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

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