A four digit number is to be formed using the digits 1 , 2 , 3 , 4 , 5 , 6 , 7 (no digit is being repeated in any number). Then, the probability that it is 4000 , is

Question

A four digit number is to be formed using the digits 1 , 2 , 3 , 4 , 5 , 6 , 7 (no digit is being repeated in any number). Then, the probability that it is > 4000 , is (A)  3/2  (B)  1/2  (C)  4/7  (D)  3/7

Tardigrade Admin · Accepted Answer

Total cases = 7 P4=840 Favourable cases =4 × 6 × 5 × 4=480 ∴ Required probability =(480/840)=(4/7)

Q. A four digit number is to be formed using the digits $1$ , $2$ , $3$ , $4$ , $5$ , $6$ , $7$ (no digit is being repeated in any number). Then, the probability that it is $> 4000$ , is

$3/2$

$1/2$

$4/7$

$3/7$

Total cases $=^{7} P_{4} = 840$
Favourable cases $= 4 \times 6 \times 5 \times 4 = 480$
$∴$ Required probability $= \frac{480}{840} = \frac{4}{7}$

Q. A four digit number is to be formed using the digits 1 , 2 , 3 , 4 , 5 , 6 , 7 (no digit is being repeated in any number). Then, the probability that it is >4000 , is

3/2

1/2

4/7

3/7