Math, asked by juvia4740, 1 year ago

In how many ways can we form a 5 digit number using digits 0,1,2,3,4,5,6,7,8,9,

Answers

Answered by Aadya16
0
Answer:
(1) : Without Repetition of digits,
27
,
216
numbers;
(2) : With Repetition,
90
,
000
numbers.
Explanation:
There are
2
Possibilities to be considered :-
Case (1) : Digits not repeated :-
Usually, we do not write the Left-most (the
1
s
t
) digit
0
, so, this digit can be any
1
out of
1
,
2
,
...
,
9
.
Thus, the
1
s
t
digit can be selected in
9
ways.
Coming to the selection of the
2
n
d
digit, keeping in mind that we can not choose the digit which we have already chosen while selecting the
1
s
t
digit, we have to select it from
10

1
=
9
digits, & this can be done in
9
ways.
Now, for the
3
r
d
, we have
10

2
=
8
choices.
For the
4
t
h
,
7
and, for the last
5
t
h
,
6
ways are there.
Finally, using the Fundamental Principle of Counting, we can form
9
×
9
×
8
×
7
×
6
=
27
,
216
five-digit nos. without repeating any digit.
Case (2): Digits repeated :-
In this case, the
1
s
t
digit can be selected in
9
ways as in the Case (1).
For the
2
n
d
place, we have
10
choices from
0
,
1
,
2
,
...
,
9
.
So, this can be done in
10
ways.
Now repetition is allowed. So, for the selection of digits for the places from
3
r
d
to the
5
t
h
, we again have
10
choices to choose from.
Accordingly, if repetition of digits is permitted, the five-digit numbers can be formed in:
9

10

10

10

10
=
90000
ways.
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