Q2) How many 5-digit positive integers exist where no two consecutive digits are the same?

A.) 9*9*8*7*6
B.) 9*9*8*8*8
C.) 9^5
D.) 9*8^4
E.) 10*9^4

IMO is C

abcde is the five digit number

so a is chosen between 1-9 so number of poosiblities is 9

and b is 0-9 10 possibilities but no consecutive so its reduced to 9

and smae for others

vishu

1) IMO 1/10

AJEET

Total number of pairs you can pick or in other words in how many ways can you pick 2 letters from 5 = 5C2 ways = 10

There is only 1 pair EE which when interchanged does not change the name

Hence the probability = 1/10

2) IMO C

The first number can be filled in 9 ways (you cannot pick 0)
2nd place - 9 numbers.
You have 10 number in total 0-9 but since you cannot choose the integer that's consecutive to the previous number you have only 9 options available.
Same logic for 3rd 4th and 5th position.
Hence the total possibilities = 9^5.

Q 1) My name is AJEET. But my son accidentally types the name by interchanging a pair of letters in my name. What is the probability that despite this interchange, the name remains unchanged?

imo 1/10