Answer: a) 9000 b) 4536 c) 4000 d) 4500
Step-by-step explanation:
Total number of digits = 10
a) The leading digit cannot be zero.
i.e The first place has only 9 choices , but the rest of places has 10 choices.
Then, the number of different 4 digit number is possible :
9 x 10 x 10 x 10 = 9000
(b) The leading digit cannot be zero and no repetition of digits is allowed.
i.e The first place has only 9 choices ( 0 is excluded) , but after the first placed occupied by a digit and 0 is included , so the choices for second place = 9
choices for third place = 8
choices for 4th place =7
Number of 4-digit number is possible = 9 x 9 x 8 x 7 = 4536
c) The leading digit cannot be zero and the number must be less than 5000.
For Leading digit , we can take only 1,2,3,4
i.e. choices for first place is 4 , but the rest of places has 10 choices.
Number of 4-digit number is possible = 4 x 10 x 10 x 19 = 4000
d) The leading digit cannot be zero and the number must be even.
i.e The first place has only 9 choices
The last place can have 2,4,6,8,0, i.e. last place has 5 choices
Number of 4-digit number is possible = 9 x 10 x 10 x 5 =4500
(a).The leading digit cannot be zero: 9000
(b). The leading digit cannot be zero and no repetition of digits is allowed: 4536
(c). The leading digit cannot be zero and the number must be less than 5000: 4000
(d). The leading digit cannot be zero and the number must be even: 4500
The Total number of digits from 0 to 9 are 10.
Now,
(a) .The leading digit cannot be zero.
The first place will have only 9 choices , but the rest of places has 10 choices.
So, the number of different 4 digit number is
= 9 x 10 x 10 x 10
= 9000
(b). The leading digit cannot be zero and no repetition of digits is allowed.
Here the first place has only 9 choices without 0.
So the choices for second place = 9
choices for third place = 8
choices for fourth place =7
So, possible number of 4-digit where the leading digit cannot be zero and no repetition of digits is allowed is
= 9 x 9 x 8 x 7
= 4536
(c) .The leading digit cannot be zero and the number must be less than 5000.
The possible Leading digit are: 1,2,3,4
So, the choices for first place = 4
And the rest of the three places has 10 choices.
So, the possible 4-digit number is
= 4 x 10 x 10 x 19
= 4000
(d). The leading digit cannot be zero and the number must be even.
Now, the first place has only 9 choices
Since the number must be even.
So the last digit can have 0, 2,4,6,8.
The last place has 5 choices
So, the possible 4-digit number
= 9 x 10 x 10 x 5
=4500
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