Q 1 How many numbers are there between 100 and 1000 such that every digit is either 2 or 9 - Maths - Permutations and Combinations

Question

Q 1 How many numbers are there between 100 and 1000 such that
every digit is either 2 or 9?
Q 2 In how many ways can the following prizes be given away to a
class of 30 students, 1st and 2nd in Maths, 1st and 2nd in physics,
1st in chem and 1st in eng
please explain me these questions and also its answers

Himanshu · Accepted Answer

1 The number is between 100 and 1000 This tells us that the
number is a three-digit number
Also, every digit has to be a 2 or a 9
The hundred's place can be filled in 2 ways (2 or 9)
The tens place can be filled in 2 ways (2 or 9)
The units place can be filled in 2 ways (2 or 9)
Therefore, the three places can be filled in 2 x 2 x 2 = 8
2
The 1st and the 2nd Maths prize can be given in 30 x 29 =
870
The 1st and the 2nd Physics prize can be given in 28 x 27 =
756
The 1st prize in Chemistry can be given in 26 = 26
The 1st prize in English can be given in 25 = 25
Total number of ways = 870 x 756 x 26 x 25 = 427518000