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(52780)   (Show Source):
You can put this solution on YOUR website! .
The RULE, the POLICY and the REQUIREMENT of this forum is
ONE and ONLY ONE problem per post.
And those who violate this rule, work against their own interests.
At this forum, I explained it just 2937 times.
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