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krakow
11-21-2004, 04:12 PM
How many 4-digit numbers begin with an odd digid and end with an even digid?

250
500
2000
2500 [clap]
5000

danielman
11-21-2004, 05:45 PM
How many 4-digit numbers begin with an odd digid and end with an even digid?

250
500
2000
2500 [clap]
5000

possibilities for 3rd digit: 1, 3, 5, 7, 9 (total = 5)
possibilities for 2nd digit: 0,1,2,3...,9 (total =10)
possibilities for 1st digit: 0,2,4,6,8 (total = 5)

possible arrangements = 5*10*5 = 2500

neokeynesian
11-22-2004, 04:10 AM
I think u have just missed the 4th digit??

possibilities for 4rd digit: 0,2,4,6,8 (total = 5)-------------------5C1
possibilities for 3rd digit: 0,1,2,3,4,5,6,7,8, 9 (total = 10)--------10C1
possibilities for 2nd digit: 0,1,2,3,4,5,6,7,8, 9 (total = 10)--------10C1
possibilities for 1st digit: 1,3,5,7,9 (total = 5)--------------------5C1

5*10*10*5=2500

danielman
11-22-2004, 04:17 AM
I think u have just missed the 4th digit??

possibilities for 4rd digit: 0,2,4,6,8 (total = 5)-------------------5C1
possibilities for 3rd digit: 0,1,2,3,4,5,6,7,8, 9 (total = 10)--------10C1
possibilities for 2nd digit: 0,1,2,3,4,5,6,7,8, 9 (total = 10)--------10C1
possibilities for 1st digit: 1,3,5,7,9 (total = 5)--------------------5C1

5*10*10*5=2500

Ooops!! :o
You're so right... I forgot a digit... (sight)

lorcar
11-22-2004, 09:52 AM
i would say in a different way...
4 digits: 10.000 number in total (0-9999)

let's take, as example, the 3 digit series (101-200)
all start with the odd digit, and HALF of the number end with an even digit. So the rate is 1/2.
BUT in our 4 digits series, ONLY HALF of the numbers start with an odd digit
So 1/2 * 1/2 = 1/4=0,25
0.25*10000= 2500

lorcar
11-23-2004, 12:11 AM
i would say in a different way...
4 digits: 10.000 number in total (0-9999)

let's take, as example, the 3 digit series (101-200)
all start with the odd digit, and HALF of the number end with an even digit. So the rate is 1/2.
BUT in our 4 digits series, ONLY HALF of the numbers start with an odd digit
So 1/2 * 1/2 = 1/4=0,25
0.25*10000= 2500
sorry
something seems wrong
then 4 digits: from 1000 to 9999
then 9000 numbers.
starting with ODD
1000
3000
5000
7000
9000

for a total of 5000 numbers. Of these, half will have even digit at the end.
--> 2500