From 3 capitals 5 consonants and 4 vowels

Number of ways of choosing $$3$$ consonants from $$5$$ consonants $$=$$ $${ \ }^{ 5 }{ C }_{ 3 }=10\text{ ways.}$$

Number of ways of choosing $$2$$ vowels from $$4$$ vowels $$=$$ $${ \ }^{ 4 }{ C }_{ 2 }=6\text{ ways.}$$

Number of ways of choosing $$1$$ capitals from $$3$$ capitals $$=$$ $${ \ }^{ 3 }{ C }_{ 1 }=3\text{ ways.}$$

This would result in $$6$$ lettered word with $$1^{\text{st}}$$ letter as capital and remaining $$5$$ letters can be anything out of vowels and consonants.

Hence, the first position is fixed by capitals and in remaining $$5$$ places $$5$$ letters can be arranged in $${\ }^{5}P_5 =5!=120 \text{ ways.}$$

Solution : Number of the ways of choosing 3 consonants from 5 consonants is=`5_C3=10`ways
Number of the ways of choosing 2 vowels from 4 vowels`=4_C2=6`ways
Number of the ways of choosing 1 capitals from 3 capitals`=3_C1=3`ways
This result would be in 6 lettered word with 1 st letter as capital and remaining 5 letters can be anything out of vowels and consonants.
so, the 1st position is fixed by the capitals and in remaining `5` letter can be arranged in `5_C5=5!=120` ways
So,number of total ways are=`10X6X3X120=21600`ways

How many words of 3 consonants and 2 vowels can be formed from 5 consonants and 4 vowels?

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