Question

How many different 3 digit numbers can be formed by using the digits 1 , 1 , 3 , 4 , 5

Answer 1

\[5P3 \]That'd be when there aren't 2 ones.

Answer 2

its not that easy :)

Answer 3

There are four choices for the first since two digits are the same, right?

Answer 4

but there are two one's in which is repeating

Answer 5

\[\LARGE{\frac{^5P_3}{2 ! }}\]

Answer 6

that is not right

Answer 7

wt is the answer?

Answer 8

I m also getting confused.

Answer 9

33

Answer 10

I m only getting this much

By using above 5 digits ; we can form 5 digit numbers in \(\LARGE{\frac{5!}{2!}=60ways}\)
Then in how many ways 3 digit numbers would be formed?

Answer 11

In first solution; I was getting 30 as answer
& In second one; I m getting 36
but not 33:\

Answer 12

I vaguely remember that it is \( \frac{n!}{(p!q!r!s!} \) ways where p+q+r+s=n.
Here we have \( \frac{5!}{(2!1!1!1!} = \frac{5!}{2!}\) = 60 ways as you said.

Answer 13

where p,q,r,s are the number of items in each group.

Answer 14

ya but how to get " in how many ways 3 digit numbers would be formed?"

Answer 15

Ohh, that's true! Silly me! I'll have to work harder.

Answer 16

me too hehe;)

Answer 17

take two cases

Answer 18

Let's start with 5P3=120/2=60.
Out of these, we will find the patterns:
X11,1X1,11X where X could be 3,4,or 5, that's overcounting by 6.
So there are 54 different numbers.

I don't like the way I do it, so will look for a different method to check.

Answer 19

1. when all d digits are different...1,3,4,5
total no of 3digits=24

Answer 20

case 2.
when there are two 1's in three digit no

Answer 21

s0 1,1,..
3rd digit can be either 3 or 4 or 5
so 3 ways and these three digits can be arranged by 3!/2! ways
so total no of 3 digits= 3*3=9

Answer 22

so total no of three digits formed by 1,1,3,4,5= 24+9=33

Answer 23

for case 1, how is the total number of digits 24?

Answer 24

4 p 3 =24

Answer 25

you have 4 different digits and have to make 3 digit nos from them..

Answer 26

i got it now. thanks

Answer 27

:)

Answer 28

nice:)

Answer 29

Yep, thanks.