The number of four-digit numbers strictly greater than 4321 that can be formed from the digits 0, 1, 2, 3, 4, 5 (allowing repetition of digits)
Answers
Answer:
311 ways
Step-by-step explanation:
We need to make a 4 digit number from 6 digits
Firstly, if we select the first digit as 5 which is our way and
second third and four digits can be any of the six digits
no. of ways of selecting second, third and forth digit = 6 ways each
No. of ways = 6×6×6 = 216 ways
Secondly, if we select the first digit as 4 (1 way)
Second digit can take values either 4 or 5 (2 ways)
No. of ways to arrange third and forth digit = 6 ways each
No. of ways = 2×6×6 = 72
Thirdly, if we select first digit as 4 (1 way)
Second digit as 3(1 way)
Third digit can only take the value (3,4,5), no. of ways = 3
forth digit can take any value from 6 digits, ∴No. of ways = 6
Total no. of ways = 3×6 = 18
Forth case, if we select first digit as 4 (1 way)
Second digit as 3(1 way)
Third digit as 2(1 way)
No. of ways by which Forth digit can take the values (1,2,3,4,5) = 5 ways
Total no. of ways = 5
No. of digits greater than 4321 = 216+72+18+5
= 311 ways