CBSE BoardEnglish MediumSTD 11 ScienceMathsCombinations2 Marks
Question
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
✓
Answer
Total vowel are = 5
Total consonants = 17
Volwels formed from 5 vowels and 17 consonants by selecting 2 vowels and 3 consonants are.
$={^\text{5}}\text{C}_{\text{2}}\times{^\text{17}}\text{C}_{\text{3}}\times5!$
$= \frac{5!}{2!3!}\times\frac{17!}{3!4!}\times120$
$=\frac{5\times4}{2}\times\frac{17\times16\times15}{3\times2}\times120$
$=10\times17\times8\times5\times120$
$=400\times17\times120$
$=6800\times120$
$=816000$
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