 Hi and how are you all today? I am Priyanka. The question says, the English alphabet has 5 vowels and 21 consonants. How many words with 2 different vowels and 2 different consonants can be formed from the alphabets? Now here we are given English. Now we have to select 2 vowels from 5 vowels which you would know. Now that means that required number of ways of selection of 2 vowels 5C to write. Therefore required number of ways of selection of 2 consonants is equal. Out of 21 we are selecting 2. Let this be the second one. So on applying the multiplication principle, the number of combinations of 2 vowels 3 consonants is equal to 1 multiplied by the second, that is 5C2 multiplied by 21C2. 2 vowels and 2 consonants, these 4 letters can also be arranged among themselves in a number of ways. So the required number of permutation equal to 4P4 that is equal to 4 factorial. Let this be the third equation. So again, applying the multiplication principle, the number of words formed using 2 vowels and 2 consonants equal to 1 multiplied by the second multiplied by the third, that is 5C2 multiplied by 21C2 multiplied by 4 factorial that is 4P4. This is equal to 5 factorial divided by 2 factorial, 5 minus 2 factorial multiplied by 21 factorial, 2 factorial, 21 minus 2 factorial multiplied by 4 factorial. That is further, 5 multiplied by 4 multiplied by 3 factorial divided by 2 factorial multiplied by 3 factorial, reduce it, multiply, 21 factorial can be written as 21 into 20 into 19 factorial divided by 2 factorial multiplied by 19 factorial multiplied by 4 factorial. This further can be simplified. This whole will be written as 10 multiplied by 210 multiplied by 24 that is 4 factorial and their product is 5040. This is our required answer for today's session. I hope you enjoyed. Use the formula of counting of combination and permutations. Take care.