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Number of strings up to length $3$ on alphabet set $\sum$ = { a,b,c,d } are :(including,string of length zero)?

$A) 16$

$B) 85$

$C) 128$

$D) 64$

edited | 60 views
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64.
+1
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oou its atmost 3 .=1+4+16+64
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if i modify the question in such a way that no repitition of same alphabet is allowed then in this case what will be answer???
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If repetition is not allowed

_       _      _   (Lenght 3$: 4*3*2 = 24$ ways)

_      _   (Length $2: 4*3=12$ ways)

_  (Length $1: 4$ ways)

(Length $0: 1$ way)

So, $24+12+4+1 = 41$

+1
yes 41 , i am also getting this.

$\underline{\hspace{0.5cm}} \ \underline{\hspace{0.5cm}} \ \underline{\hspace{0.5cm}}$ 4 options to fill each blank = $4^3 = 64$

$\underline{\hspace{0.5cm}} \ \underline{\hspace{0.5cm}}$ $=4^2 = 16$

$\underline{\hspace{0.5cm}} = 4^1 = 4$

$1$

$64 + 16 + 4 + 1 = 85$
by Boss (35.4k points)
selected
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Wow,it's a easy method.

Thanks Brother

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