explaination and solution plzzzzz....
Answers
Hey there!!
______________________________
The correct answer is C=780
Answer : Option C
Explanation :
Given that the numbers should not exceed 10000
Hence numbers can be 1 digit numbers or 2 digit numbers or 3 digit numbers
or 4 digit numbers
Given that repetition of the digits is allowed.
A. Count of 1 digit numbers that can be formed
using the 5 digits (2,4,5,6,8) (repetition allowed)
The unit digit can be filled by any of the 5 digits (2,4,5,6,8)
5
Hence the total count of 1 digit numbers that can be formed
using the 5 digits (2,4,5,6,8) (repetition allowed) = 5 ---(A)
B. Count of 2 digit numbers that can be formed
using the 5 digits (2,4,5,6,8) (repetition allowed)
Since repetition is allowed, any of the 5 digits(2,4,5,6,8) can be placed
in unit place and tens place.
5 5
Hence the total count of 2 digit numbers that can be formed
using the 5 digits (2,4,5,6,8) (repetition allowed) = 52 ---(B)
C. Count of 3 digit numbers that can be formed
using the 5 digits (2,4,5,6,8) (repetition allowed)
Since repetition is allowed, any of the 5 digits (2,4,5,6,8) can be placed
in unit place , tens place and hundreds place.
5 5 5
Hence the total count of 3 digit numbers that can be formed
using the 5 digits (2,4,5,6,8) (repetition allowed) = 53 ---(C)
D. Count of 4 digit numbers that can be formed
using the 5 digits (2,4,5,6,8) (repetition allowed)
Since repetition is allowed, any of the 5 digits (2,4,5,6,8) can be placed
in unit place, tens place, hundreds place and thousands place
5 5 5 5
Hence the total count of 4 digit numbers that can be formed
using the 5 digits (2,4,5,6,8) (repetition allowed) = 54 ---(D)
From (A), (B), (C), and (D),
total count of numbers not exceeding 10000 that can be made
using the digits 2,4,5,6,8 (with repetition of digits)
= 5 + 52 + 53 + 54
=5(54–1)5−1
[∵ Reference: Sum of first n terms in a geometric progression (G.P.) ]
=5(625–1)4=5(624)4=5×156=780
______________________
Thank you
Hope it helps you! ヅ
✪ Be Brainly ✪