The number of five digit numbers that contain 7 exactly once is equal to

Step-by-step solution

(i) Case Ι → 7 X _ X _ X _ X _ at places marked X , we can place 0 to 9 , except 7 , in 9 × 9 × 9 × 9 = 9 4 ways (ii) Case Ι Ι → X _ Y _ 7 _ Y _ Y _ If 7 is at some other place, first place marked X can be filled in 8 ways ( 0 and 7 not allowed) and places marked Y can be filled in 9 ways. 7 can be placed at any of the four places in 4 × 8 × 9 3 ways ⇒ Required number of ways = 9 4 + 32 × 9 3 = 41 9 3 .