Question

Anbu asks Anjali to guess a five digit odd number. He gives the following hints.
● The digit in the 1000s place is less than 5
● The digit in the 100s place is greater than 6
● The digit in the 10s place is 8
What is Anjali’s answer? Does she give more than one answer?

Answer 1

one answer only she gave but in different way

Answer 2

Answer:

There are 540  possibilities of five-digit odd number that could be had in  Anjali's mind.

Step-by-step explanation:

Anjali can first design the five-digit place value chart

Means : Ten Thousand’s place Thousand’s place     Hundred’s place Ten’s place      Unit place

a) To be a five-digit number, the digit in the ten thousandth place can be anything greater than 0. So, there are 9 possibilities for a digit to occur in the ten thousandth place.

b) Given that the digit in the thousandth place should be less than 5. So, the digit can be either 0, 1, 2, 3 or 4. So there are four possibilities for a digit to occur in the thousandth place

c) Given that the digit in the hundredth place should be greater than 6. So, the digit can be either 7, 8 or 9. So there are three possibilities for a digit to occur in the hundred’s place

d)  The digit in the tenth’s place is always 8. So, there is only one possibility for a digit to occur in the tenth place

e) As the five-digit number should be an odd number, the digit in unit’s place should be either 1, 3, 5, 7 or 9. So there are five possibilities for a digit to occur in the unit place

The number of five-digit odd numbers that could be formed is,

                              $9 \times 4 \times 3 \times 1 \times 5 = 540$ five-digit odd numbers could be guessed by Anjali.