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## three-digit number.

Q.1. How many three digit odd numbers can be formed using the digits 1,2,3,4,5,6 and 7?

Q.2. A five digit number is chosen at random, What is the probability that the product of the digits is an even number?

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## Re: three-digit number.

Originally Posted by awais
Q.1. How many three digit odd numbers can be formed using the digits 1,2,3,4,5,6 and 7?

Q.2. A five digit number is chosen at random, What is the probability that the product of the digits is an even number?
Q1. 7*7 *4 = 49*4 = 196

(if no repetition, then 6*5 *4 =30*4 = 120)

Q2.
6561*9
729*7
81*5
9*3
Total=64584

Total 5digit numbers=90000

P = 64584/90000 ~ 0.71

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## Re: three-digit number.

Q1
a) with repetition
7*7*4=196

b)without repetition
first two digits -both even 3!/1!=6 times number of odd digits left *4 =24
first two digits -both odd 4!/2!=12 times number of odd digits left *2 =24
first two digits -one even one odd 3*4=12 times number of odd digits left *3=36

asw =84

Q2.
in order to have product of any number of numbers even, one of numbers must be even.

The probability that all five digits are odd (assuming that 0 is even) is:
(5/10)^5 = (1/2)^5 =1/32 the probability that at least one of digits is even =31/32

asw 31/32

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## Re: three-digit number.

Q#1
1)with repetition
7 * 7* 4 = 196

2)without repetition
a) odd odd odd = 4*3*2 = 24
b) odd even odd = 4* 3* 3 = 36
c) even odd odd = 3 * 4* 3 = 36
d) even even odd = 3* 2* 4= 24
Total 120

Q#2
1- ( probability that all numbers are odd)
1 - ( (1/2)^5) = 31/32

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## Re: three-digit number.

yap. second is 31/32
just learned th method segregation from another thread.

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## Re: three-digit number.

Originally Posted by thebullfighter
Q1.
(if no repetition, then 6*5 *4 =30*4 = 120)
Hey bull, how did you get this ?

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## Re: three-digit number.

Originally Posted by shaq
Hey bull, how did you get this ?
u testin' me or u din't actually get it... gotta be kiddin me, i learned P&C & P analysin ur answers & studyin links provided by u..

Q.1. How many three digit odd numbers can be formed using the digits 1,2,3,4,5,6 and 7?

odd no.s-- 1,3,5,7

Case 1-- Last digit is 1 (fixed)

so other positions can be filled in (7-1=6): 6*5 ways

similarly for other 3 odd numbers.
Hence, 6*5 *4=120

how did i do???

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## Re: three-digit number.

Answer for the first question, 7*7*4= 196
For the second, 1- ( 5/10 )^5 or 1 - (1/2)^5 =

Hey Bullfighter good job for solving q.1 without repetition.

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## Re: three-digit number.

Originally Posted by thebullfighter
u testin' me or u din't actually get it... gotta be kiddin me, i learned P&C & P analysin ur answers & studyin links provided by u..

Q.1. How many three digit odd numbers can be formed using the digits 1,2,3,4,5,6 and 7?

odd no.s-- 1,3,5,7

Case 1-- Last digit is 1 (fixed)

so other positions can be filled in (7-1=6): 6*5 ways

similarly for other 3 odd numbers.
Hence, 6*5 *4=120

how did i do???
Good job bull. I split it up differently ( but yours was simpler).
Kudos to you kid..

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## Re: three-digit number.

heeey... thanx man. (shaq just praised mine over 'shaq's' own method, tht too for P.. now, this is an honour.)