Maths Solve the Following Question.(2 Marks)

Between any set of digits, the greatest number is possible when digits are arranged in descending order. ∴ 7432 is the greatest number, formed from the digits 2, 3, 4, 7. Since a 4-digit number is to be formed from the digits 2, 3, 4, 7, where repetition of the digit is not allowed, 1000’s place digit can be selected in 4 ways, 100’s place digit can be selected in 3 ways, 10’s place digit can be selected in 2 ways, Unit’s place digit can be selected in 1 way. ∴ Total number of numbers not exceeding 7432 that can be formed with the digits 2, 3, 4, 7 = Total number of four-digit numbers possible from the digits 2, 3, 4, 7 = 4 × 3 × 2 × 1 = 24

Numbers between 100 and 1000 are 3-digit numbers. A 3-digit number is to be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, where the unit place digit is 4. Unit’s place digit is 4. ∴ it can be selected in 1 way only. 10’s place digit can be selected in 10 ways. For a 3-digit number, 100’s place digit should be a non-zero number. ∴ 100’s place digit can be selected in 9 ways. ∴ By using the fundamental principle of multiplication, total numbers between 100 and 1000 which have 4 in the units place = 1 × 10 × 9 = 90.

A 3-digit number is to be formed from the digits 2, 3, 4, 5, 6 where digits can be repeated. ∴ Unit’s place digit can be selected in 5 ways. 10’s place digit can be selected in 5 ways. 100’s place digit can be selected in 5 ways. ∴ By using fundamental principle of multiplication, total number of 3-digit numbers = 5 × 5 × 5 = 125

A two-letter word is to be formed out of the letters of the word SPACE. (i) When repetition of the letters is allowed 1st letter can be selected in 5 ways. 2nd letter can be selected in 5 ways. ∴ By using the fundamental principle of multiplication, the total number of 2-letter words = 5 × 5 = 25 (ii) When repetition of the letters is not allowed 1st letter can be selected in 5 ways. 2nd letter can be selected in 4 ways. ∴ By using the fundamental principle of multiplication, the total number of 2-letter words = 5 × 4 = 20

A signal is generated from 2 flags and there are 4 flags of different colours available. ∴ 1st flag can be any one of the available 4 flags. ∴ It can be selected in 4 ways. Now, 2nd flag is to be selected for which 3 flags are available for a different signal. ∴ 2nd flag can be anyone from these 3 flags. ∴ It can be selected in 3 ways. ∴ By using the fundamental principle of multiplication, total no. of ways a signal can be generated = 4 × 3 = 12 ∴ 12 different signals can be generated.

There are 30 boys and 20 girls. A teacher can select any boy as a class monitor from 30 boys in 30 different ways and he can select any girl as a class monitor from 20 girls in 20 different ways. ∴ by the fundamental principle of addition, the total number of ways a teacher can select a class monitor = 30 + 20 = 50 Hence, there are 50 different ways to select a class monitor.