Given-the-number-of-consisting-of-4-digits-abcd-such-that-a-b-c-d-is-A-495-B-385-C-275-D-165-E-55-

Question Number 198283 by cortano12 last updated on 16/Oct/23

Given the number of consisting

of 4 digits abcd such that

a ⩽ b ⩽ c ⩽ d is \dots

(A) 495 (B) 385 (C) 275

(D) 165 (E) 55

Commented by mr W last updated on 19/Oct/23

(A) 495

g e n e r a l l y w i t h k d i g i t s : \frac{(k + 8)!}{8! k!}

s e e Q 117061

Answered by MM42 last updated on 16/Oct/23

{a, b, c, d} \to (\begin{matrix} 9 \\ 4 \end{matrix}) = 126

{a, a, b, c} \to (\begin{matrix} 9 \\ 3 \end{matrix}) \times 3 = 252

{a, a, b, b} \to (\begin{matrix} 9 \\ 2 \end{matrix}) = 36

{a, a, a, b} \to (\begin{matrix} 9 \\ 2 \end{matrix}) \times 2 = 72

{a, a, a, a} \to 9

a n s = 495 ✓ \to A

Commented by cortano12 last updated on 17/Oct/23

why (a, a, a, b) = (\begin{matrix} 9 \\ 2 \end{matrix}) \times 2 ?

Commented by mr W last updated on 17/Oct/23

(a, b, b, b) a n d (a, a, a, b)

Commented by MM42 last updated on 17/Oct/23

\underset{―}{\underset{⏟}{⋚}}

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