Question

Heya...❤❤brainliacs....

Count the numbers between 999 and 10,000 subject to the condition that there are 

(i)no restriction. 

(ii) no digit is repeated. 

(iii) at least one of the digits is repeated

Answer 1

(Find the numbers between 999 and 10000

⇒ It is a 4-digit number

.

Question (i): No Restriction:

thousandths place = all possible digits 1-9, (excluding 0) = 9 possible digits

hundredths place = all possible digit 0-9 = 10 possible digits

tens place = all possible digit 0-9 = 10 possible digits

ones place = all possible digit 0-9 = 10 possible digits

Total number of possible combination = 9 x 10 x 10 x 10 = 9000

Answer: There are 9000 combinations

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Question (ii): No repeats

thousandths place = all possible digits 1-9, (excluding 0) = 9 possible digits

hundredths place = all possible digit 0-9, excluding the one in the thousands place = 9 possible digits

tens place = = all possible digit 0-9, excluding the one in the thousands place and the hundredths place = 8 possible digits

ones place = all possible digit 0-9, excluding the one in the thousands place, hundredths place and tens places = 7 possible digits

Total number of possible combinations = 9 x 9 x 8 x 7 = 4536

Answer: There are 4536 combinations

.

Question (iii): At least one repeat:

Total possible combinations = 9000 - 4536 = 4464

Answer: There are 4464 combinations

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