In how many ways can $4$ letters be selected from the word $^{'} E X A M I N A T I O N^{'}$ ?

120

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136

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110

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135

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Solution

The correct option is B $136$
$E X A M I N A T I O N$
$E ⟶ 1$
$X ⟶ 1$
$A ⟶ 2$
$M ⟶ 1$
$I ⟶ 2$
$N ⟶ 2$
$T ⟶ 1$
$O ⟶ 1$
Selecting $4$ letters
Case : 1 All distict : $^{8} C_{4}$ Ways $= 70$ Ways
Case : 2 $2$ letter alike , $2$ distict
$\Rightarrow^{3} C_{1} \times^{7} C_{2} = 63$
Case : 3 $2$ letter alike $2$ letter
$=^{3} C_{2} = 3$
Solution $: 70 + 63 + 3 = 136$

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