The number of numbers, lying between 99 and 1000 that can be made from the digits 2,3,7,0,8 and 6 when the digits occur only once in each number, is

Question

The number of numbers, lying between 99 and 1000 that can be made from the digits 2,3,7,0,8 and 6 when the digits occur only once in each number, is (A) 100 (B) 90 (C) 120 (D) 80

Tardigrade Admin · Accepted Answer

Required number of numbers =6P3-5 text​P2=120-20=100 . Since, between 99 &1000 , the numbers are of 3 digits, but those numbers should be omitted in which 0 comes at hundreds place.

Q. The number of numbers, lying between $99$ and $1000$ that can be made from the digits $2, 3, 7, 0, 8$ and $6$ when the digits occur only once in each number, is

$100$

$90$

$120$

$80$

Required number of numbers $=^{6} P_{3} -^{5} P_{2} = 120 - 20 = 100$ .
{Since, between $99&1000$ , the numbers are of $3$ digits, but those numbers should be omitted in which $0$ comes at hundreds place}.

Q. The number of numbers, lying between 99 and 1000 that can be made from the digits 2,3,7,0,8 and 6 when the digits occur only once in each number, is

100

90

120

80