Question Number 103300 by bramlex last updated on 14/Jul/20

many positive five−digit  integers with the first number 1  and there are three equal  numbers ?  (a) 810    (b) 720    (c)120  (d) 60     (e) 20

Answered by bemath last updated on 14/Jul/20

case(1) 1_11xx =9×((4!)/(2!.2!)) = 54   case(2)1_11xy = C_2 ^9 ×((4!)/(2!)) = 432  case(3)1_xxxy = 9×8×((4!)/(3!)) = 288  case(4)1_1xxx= 9×((4!)/(3!))=36  totally = 54+432+288+36 = 810

Commented bybemath last updated on 14/Jul/20

thank you

Commented byjohn santu last updated on 14/Jul/20

correction   case(3) 1_xxxy = 9×8×((4!)/(3!)) =  288 .  totally = 54+432+288+36  =810. (answer A) (JS ⊛)