Question

5. How many odd numbers less than 4000 may be formed with the digits 1, 2, 3, 4 and
6 if digits can be repeated.
[Hints: (a) Number of 1 digit odd number = 2
(b) Number of 2 digit odd number = 2 * 5 = 10
(c) Number of 3 digit odd number = 2 x 5 x 5 = 50
(d) Number of 4 digit odd number = 2 x 3 x 5 x 5 = 150]​

Answer 1

Answer:

we know that in unit digit is odd then the whole no. is odd,always having 3 and 1 in unit digit according to question

Step-by-step explanation:

no. odd no. between 1 to 10 is 2

therefore no. of odd no. will equal to

4000/10 ×2

800

.Hint was not good..

Answer 2

Given : Odd Numbers less than 4000 may be formed with the digits 1, 2, 3, 4 and  6.  digits can be repeated.

To Find : How Many numbers

Solution:

digits 1, 2, 3, 4 and  6

odd numbers with end with 1 or 3  in 2 ways

1 Digit Numbers  = 2    ( 1 and 3 )

2 Digit numbers  = X1  or X3

X can be in 5 ways  ( 1, 2, 3, 4 or 6 )  

= 5 x 2

= 10 Ways

3 Digit numbers  = YX1  or YX3

X , Y each  can be in 5 ways  ( 1, 2, 3, 4 or 6 )  

= 5 x 5 x 2

= 50 Ways

4 Digit numbers  = ZYX1  or ZYX3

X , Y each  can be in 5 ways  ( 1, 2, 3, 4 or 6 )  

Z < 4  as number is less than 4000  

Z can be in 3 ways  ( 1 , 2 or 3)

= 3 x 5 x 5 x 2

= 150 Ways

Total  = 2 + 10  + 50 + 150

= 212

212 odd numbers less than 4000 may be formed with the digits 1, 2, 3, 4 and  6 if digits can be repeated.

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