How many words of 4 consonants and 3 vowels can be formed out of 8 consonants and 5 vowels?
There are 3 consonants and 3 vowels. Show
= `((8 xx 7 xx 6 xx 5))/((4 xx 3 xx 2)) xx ((3 xx 2 xx 1))/((2 xx 1)` = 70 × 3 4 consonants can be selected from 8 consonants in 8C4 ways and 2 vowels can be selected from 3 vowels in 3C2 ways. ∴ the number of words with 4 consonants and 2 vowels = 8C4 × 3C2 = `(8!)/(4!4!) xx (3!)/(2!1!)` = `(8 xx 7 xx 6 xx 5)/(4 xx 3 xx 2 xx 1) xx (3 xx 2!)/(2!)` = 70 × 3 = 210 Now each of these words contains 6 letters which can be arranged in 6P6 = 6! ways. ∴ the total number of words that can be formed with 4 consonants and 2 vowels = 210 × 6! = 210 × 6 × 5 × 4 × 3 × 2 × 1 = 151200. Complete step-by-step solution: 3 consonants BCD. Choose 2 consonants, no repetition. Form different words from the chosen consonants and vowels. Choose 2 consonants, 3 ways - BC, BD, CD. Different groups with 2 consonants and 2 vowels, 3x3 = 9. BCAE, BCAI, BCEI, BDAI, BDAI, BDEI, CDAE, CDAI, CDEI. Different words from 4 character set such as BCAE, 4! = 4x3x2x1 = 24. BCAE, BCEA, BACE, BAEC, BECA, BEAC. Total 4 character words from 2 different consonants and 2 different vowels would be 9x24 = 216. Apply to above. 7C3 x 4C2 x 5! = 25200. More difficult would be when repetitions are allowed in consonants and vowels. How many words of 4 consonants and 3 vowels can be?∴ Required number of words =12C4∗4C3∗7! =9979200.
How many words of 3 consonants and 3 vowels can be formed from 8 consonants and 4 vowels?∴ The required result will be 40320.
How many words can be formed by 2 vowels and 3 consonants out of 4 vowels and 7 consonants?Out of 7 Consonants and 4 vowels, words are to be formed by involving 3 consonants and 2 vowels. The number of such words are formed is: A. 25200.
How many words of 3 consonants and 2 vowels can be formed from 5 consonants and 4 vowels?From 5 consonants and 4 vowels, how many words can be formed by using 3 consonants and 2 vowels. A. 9440.
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