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6.Permutation and Combination
normal
Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to
A
$210$
B
$237$
C
$247$
D
$227$
Solution
$\mathrm{S}^{1} \mathrm{A}^{3} \mathrm{H}^{1} \mathrm{R}^{2} \mathrm{N}^{1} \mathrm{P}^{1} \mathrm{U}^{1}$
$3$ alike $+3$ different $+2$ alike, $1$ different
${\,^1}{{\rm{C}}_1} \times \frac{{3!}}{{3!}} + {\,^7}{{\rm{C}}_3} \times 3! + {\,^2}{{\rm{C}}_1} \times {\,^6}{{\rm{C}}_1} \times \frac{{3!}}{{2!}}$
$1+210+36=247$
Standard 11
Mathematics
