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6.Permutation and Combination
hard
મૂળાક્ષરો $a, b, c$ નો ઉપયોગ કરી ને ચાર મૂળાક્ષરોના કેટલા શબ્દો બનાવી શકાય કે જેમાં બધાજ મૂળાક્ષરો આવે .
A
$30$
B
$36$
C
$81$
D
$256$
(KVPY-2019)
Solution
(b)
Out of given three letters $a, b, c$, we will repeat exactly one of the letter and we can do this in ${ }^3 C_1$ ways.
Now, we have four letters and out of these four letters two are identical, so number of ways to arrange these four letters is $\frac{4 !}{2 !}$.
So, the number of four letter words that can be formed with letters $a, b, c$ such that all three letters occur is
${ }^3 C_1 \times \frac{4 !}{2 !}=36$
Standard 11
Mathematics
