10.11.2: Counting binary strings ***DISCRETE MATH, PLEASE ONLY ANSWER IF YOU CAN
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Question
10.11.2: Counting binary strings
***DISCRETE MATH, PLEASE ONLY ANSWER IF YOU CAN ANSWER EVERY SINGLE QUESTION.
1)Count the number of binary strings of length 10 subject to each of the following restrictions.
(a)The string has at least one 1.
(b)The string has at least one 1 and at least one 0.
(c)The string contains exactly five 1's or it begins with a 0.
2)A dozen cookies are selected at a bakery. There are six varieties of cookies: chocolate chip, sugar, ginger, oatmeal raisin, M&M, and snickerdoodles. How many ways are there to select the cookies so that there is at least one chocolate chip or M&M cookie in the selection?
3)A five-card hand is selected from a standard playing deck. How many hands have at least one Queen or Jack?
Explanation / Answer
3) 5 five card is selected.
P(Atleast 1 Q or J)
= 1- P( no Queen or jAck)
= 1- P( select non Queen or Non Jack card)
= 1- 44C5/52C5
= 0.418
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