Question

Seven digit numbers are made from using all digits repetition of digits is allowed. Then the probability that the sum of digits of number is 61, is

• A. $\frac { 28 } { 10 ^ { 7 } }$
• B. $\frac { 28 } { 9 \times 10 ^ { 6 } }$
• C. $\frac { 10 ^ { 4 } } { 9 ^ { 6 } }$
• D. $\frac { 9 ^ { 4 } } { 10 ^ { 7 } }$

Answer 1

Answer: (B)

$\frac { 28 } { 9 \times 10 ^ { 6 } }$

Answer 2

Total seven digit no. = 9 × 10⁶

Numbers sum of whose digit is 61 is made by

(9, 9, 9, 9, 9, 9, 7) or (9, 9, 9, 9, 9, 8, 8)

Total favourable no. are = $\frac { 7 ! } { 6 ! }$+ $\frac { 7 ! } { 5 ! 2 ! }$ = 7 + 21 = 28

Probability = $\frac { 28 } { 9 \times 10 ^ { 6 } }$