Question

How many 5-digit odd whole numbers are there if there is no leading zero, the third digit must be 6, and the second digit must be greater than zero and divisible by 4. No digits may repeat. PLEASE HELP. Thank you!

Answer 1

third digit can be filled be in only one way i.e 6

second digit must be greater than zero and divisible by 4,so can be filled in two ways i.e. 4,8

last digit should be odd as odd numbers are to be find,so number of ways to fill last place are(1,3,5,7,9) =total 5 ways

now, three digits had already been placed so,for first place, only 7 digits left out of 10 digits

but 0 cant be placed on first digit so, total ways of filling first place =6

now, 4 th place can be filled in 6 ways(as total 6 digits left after filling all places)

so, total number of 5-digit whole number = 6*2*1*6*5=360 numbers

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