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અંગ્રેજી વર્ણમાળામાં $5$ સ્વરો અને $21$ વ્યંજનો છે. મૂળાક્ષરોમાંથી $2$ ભિન્ન સ્વરો અને $2$ ભિન્ન વ્યંજનો દ્વારા કેટલા શબ્દો બનાવી શકાય ?
$50400$
$50400$
$50400$
$50400$
Solution
$2$ different vowels and $2$ different consonants are to be selected from the English alphabet. since there are $5$ vowels in the English alphabet, number of ways of selecting $2$ different vowels from the alphabet $=\,^{5} C_{2}=\frac{5 !}{2 ! 3 !}=10$
since there are $21$ consonants in the English alphabet, number of ways of selecting $2$ different consonants from the alphabet $=\,^{21} C_{2}=\frac{21 !}{2119 !}=210$
Therefore, number of combinations of $2$ different vowels and $2$ different consonants $=10 \times 210=2100$
Each of these $2100 $ combinations has $4$ letters, which can be arranged among themselves in $4 !$ ways.
Therefore, required number of words $=2100 \times 4 !=50400$
