If 4-digit numbers greater than 5,000 are randomly formed from the digits 0,1,3,5 and 7. What is the probability of forming a number divisible by 5 when (i) the digits are repeated (ii) the repetition of digits is not allowed?

Question

If 4-digit numbers greater than 5,000 are randomly formed from the digits 0,1,3,5 and 7. What is the probability of forming a number divisible by 5 when (i) the digits are repeated (ii) the repetition of digits is not allowed?

Filo · Accepted Answer

(i) When the digits are repeatedSince four-digit numbers greater than 5000 are formed the leftmost digit is either 7 or 5The remaining 3 places can be filled by any of the digits 0, 1, 3, 5, or 7 as repetition of digits is allowed∴ Total number of 4- digit numbers greater than 5000 = 2×5×5×5×=250A number is divisible by 5 if the digit at its units place is either 0 or 5∴ Total number of 4-digit numbers greater than 5000 that are divisible by 5=2×5×5×5×2=100Thus the probability of forming a number divisible by 5 when the digits are repeated is 250100​=52​(ii) When repetition of digits is not allowedThe thousands place can be filled with either of the two digits 5 or 7The remaining 3 places can be filled with any of the remaining 4 digits∴ Total number of 4-digit numbers greater than 5000=2×4×3×2=48When the digit at the thousands place is 5 the units place can be filled only with 0 and the tens and hundreds places can be filled with any two of the remaining 3 digits∴ Here number of 4-digit numbers starting with 5 and divisible by 5=3×2=6When the digit at the thousands place is 7 the units place can be filled in two ways (0 or 5)  and the tens and hundreds places can be filled with any two of the remaining 3 digits∴ Here number of 4-digit numbers starting with 7 and divisible by 5 = 1×2×3×2= 12∴ Total number of 4-digit numbers greater than 5000 that are divisible by 5 = 6 + 12=18Thus the probability of forming a number divisible by 5 when the repetition of digits is not allowed is 4818​=83​

Question Text	If $4$ -digit numbers greater than $5, 000$ are randomly formed from the digits $0, 1, 3, 5$ and $7$ . What is the probability of forming a number divisible by $5$ when (i) the digits are repeated (ii) the repetition of digits is not allowed?
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If $4$ -digit numbers greater than $5, 000$ are randomly formed from the digits $0, 1, 3, 5$ and $7$ . What is the probability of forming a number divisible by $5$ when (i) the digits are repeated (ii) the repetition of digits is not allowed?

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