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2. Of the three-digit integers greater than 700, how many have two digits equal to each other and the remaining digit different? A) 90 B) 82 C) 80 D) 45 E) 36

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  1. 5 June, 08:29
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    correct option is C) 80

    Step-by-step explanation:

    given data

    three-digit integer > 700

    solution

    As we know that 3 digit number can be here as 3 patterns

    1. all 3 digit distinct

    2. 2 a like and 3rd is different

    3. all 3 digit are a like

    so here

    we get here (2.) 2 a like and 3rd is different

    that is Total - (1) - (3)

    here total 3 digit number greater than 700 as 700 to 999

    total = 299

    when all 3 digit distinct, 1st digit have only 3 values they are 7, 8, 9

    so they will as

    all 3 digit distinct = 3 * 9 * 8

    all 3 digit distinct = 216

    and

    when all 3 alike they are

    all 3 alike = 3

    as they is 777, 888 and 999

    so that two digits equal to each other and the remaining digit different is

    = 299 - 216 - 3

    =80

    so correct option is C) 80
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