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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

Respuesta :

Answer:

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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