permutations (1 Viewer)

[ozidolroks]

hi can someone explain to me how to do this question ?

a 3 digit number is to be made from the digits 2,3,4,5,6,7.

In how many ways can an even number be made from these digits?
How many number over 600 can be made ?

 

[lolokay]

1) for the number to be even, the last digit must be 2, 4 or 6
so pick this number first (3 ways). there are then 5 ways to pick one of the other digits, and 4 ways to pick the other -> so 5*4*3 = 60

2) if the number has 3 digits, the first digit must be 6 or 7. there are then 5 digits to choose for the second digits, then 4 for the third.

so 2*5*4=40

 

[addikaye03]

hi can someone explain to me how to do this question ?

a 3 digit number is to be made from the digits 2,3,4,5,6,7.

In how many ways can an even number be made from these digits?
How many number over 600 can be made ?

1) 6x5x2=60ways
2)2x5x4=40ways

if thats right then i will explain

 

[ozidolroks]

that is right

 

[addikaye03]

lolokay, can you please explain that even though my answer is correct its not the best way, and explain your way. Thanks mate.

 

[ozidolroks]

How would you do this question ?

How many numbers can be made using digits 1 to 4, with no digit allowed more than once? ( number can have any number of digits)

How many numbers less than 100 can be made ?

 

[lolokay]

1) is just 4!/0! + 4!/1! + 4!/2! + 4!/3!
= 24 + 24 + 12 + 4 = 64

2) less than 100 means 1 or 2 digits, so 12 + 4 = 16

 

[ozidolroks]

why ?

 

[Timothy.Siu]

why ?

why to wich part?

since it can be any number of digits but no repititions

u can have 4+4x3+4x3x2+4x3x2x1 numbers by putting numbers into each spot...where each number is the number of choices u have

2nd part to be less than 100 it has to be a 2 digit or 1 digit number, so 4+4x3

 

[jeff.wong]

First part you can also do [i think]:
6C3 [picking 3digits] x 3! [arrangement of 3 digits] x 1/2 [since theres 3 odd and 3 even numbers 1/2 the time it would be odd and rest even] = 60