Question

Find the number of 4-digit numbers that can be formed using the digits 1 , 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

Answer 1

total digits = 5

_ _ _ _ is a four digit number

at units place we have 5 options (we can write 1,2,3,4 or 5 say 5)

at tens place we have 4 options( we can write 1,2,3 or 4 but not 5 since repetition not allowed)

similarly at hundredth and thousand place we have 3 and 2 options respectively

hence total 4 digit numbers formed = 5*4*3*2 = 120

now for number to be even the units place digit should be 2 or 4

so fix the units place number

case 1: let the units place number be 2

so for tens place we have 4 options(1,3,4 and 5) similarly because repetition is not allowed, for hundredth and thousandth place we have 3 and 2 options respectively

hence total 4 digit numbers with units place 2 i.e. even numbers = 4*3*2 = 24

case 2: now let the units place number be 4

so for tens place we have 4 options(1,2,3 and 5) similarly because repetition is not allowed, for hundredth and thousandth place we have 3 and 2 options respectively

hence total 4 digit numbers with units place 4 i.e. even numbers = 4*3*2 = 24

total 4 digit even numbers = 24 + 24 = 48

Answer 2

Answer:

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