Answer to Question #199329 in Statistics and Probability for Bahawal tahir

Question #199329

(a) How many different positive three-digit whole numbers can be formed from the four digits 2, 6, 7, and 9 if any digit can be repeated?

(b) How many different positive whole numbers less than 1000 can be formed from 2, 6, 7, 9 if any digit can be repeated? 

(c) How many numbers in part (b) are less than 680 (i.e. up to 679)? 

(d) What is the probability that a positive whole number less than 1000, chosen at random from 2, 6, 7, 9 and allowing any digit to be repeated, will be less than 680?


1
Expert's answer
2021-05-28T09:52:24-0400

a) Repetitions are allowed

n=4,r=3n=4, r=3


nr=43=64n^r=4^3=64

b) Repetitions are allowed

n=4,r=1n=4, r=1


nr=41=4n^r=4^1=4

n=4,r=2n=4, r=2


nr=42=16n^r=4^2=16

n=4,r=3n=4, r=3


nr=43=64n^r=4^3=64

Then


4+16+64=844+16+64=84



c) Numbers from 692692 to 699699


692,696,697,699692, 696, 697, 699

Numbers from 722722 to 799799

n=4,r=2n=4, r=2


nr=42=16n^r=4^2=16


Numbers from 922922 to 999999

n=4,r=2n=4, r=2


nr=42=16n^r=4^2=16

Then numbers less than 680


84(4+16+16)=5884-(4+16+16)=58

d)

P(<680)=5884=29420.690476P(<680)=\dfrac{58}{84}=\dfrac{29}{42}\approx0.690476


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