please use Pigeonhole Principle, discrete math There are 121.4 million people in
ID: 3121120 • Letter: P
Question
please use Pigeonhole Principle, discrete math
There are 121.4 million people in the United States who earn an annual income that is at least $10,000 and less than $1,000,000. Annual income is rounded to the nearest dollar. Show that there are 123 people who earn the same annual income in dolars 2) Show that among a group of 621 people, there are at least 21 who are bom on the same day of the month (e.g., the 21st or the 12th, etc. I the same fact true if there are only 620 people? A team wishes to purchase 10 shirts of the same color. A store sells shirts in 3 different colors. What must the inventory of the store be in order to conclude that there are at least 10 shirts in one of the three colors? How many people must be selected to make sure that there are at least 20 who are bom in the same month?Explanation / Answer
a) As total number of integers b/w $10,000 and 1,000,000 =990000
hence even if each integer has equal values then 121.5/990000 =122.66 will have same annual income.
hence at least 122 people are there who earn the same annual income in dollars
b) There are total 31 probable days a man can born in hence with equal distribution number of birhtday =621/31 =20
and we have 1 perdon to distribute among 31 days which makes at least 21 born on same day of the month
now if 620 ppl are there then for equal distribution on days we have one possibilty that 20 people are born on same day. Hence the same is not true if there are only 620 people
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