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-

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

c a s e (1) 1_11 x x = 9 \times \frac{4!}{2! . 2!} = 54

c a s e (2) 1_11 x y = C_{2}^{9} \times \frac{4!}{2!} = 432

c a s e (3) 1_x x x y = 9 \times 8 \times \frac{4!}{3!} = 288

c a s e (4) 1_1 x x x = 9 \times \frac{4!}{3!} = 36

t o t a l l y = 54 + 432 + 288 + 36 = 810

Commented by bemath last updated on 14/Jul/20

t h a n k y o u

Commented by john santu last updated on 14/Jul/20

c o r r e c t i o n

c a s e (3) 1_x x x y = 9 \times 8 \times \frac{4!}{3!} =

288 .

t o t a l l y = 54 + 432 + 288 + 36

= 810 . (a n s w e r A) (J S ⊛)