Question

What is the total number of permutations of the word MONDAY, if all the vowels and consonants are together? ​

Answer 1

Answer:

So, permutations of four different letters are to be explored such there is at least one vowel.

Now, four letter word can be formed in two patterns.

Pattern-1: Using three consonants and one vowel. Three consonants can be chosen in (4C3) ways = 4 ways and one vowel can be chosen in (2C1) ways = 2 ways; and the four chosen letters can be permuted in (4!) ways = 24 ways. So, as per Pattern-1; there are (4 * 2 * 24) = 192 permutations.

Pattern-2: Using two consonants and two vowels. Two consonants can be chosen in (4C2) ways = 6 ways and two vowels can be chosen in (2C2) way = 1 way; and four chosen letters can be permuted in (4!) ways = 24 ways. So, as per Pattern-2; there are (6 * 1 * 24) = 144 permutations.

Thus, combining Pattern-1 and Pattern-2; there shall be (192 + 144) = 336 permutations.

Step-by-step explanation:

$Brainliest$

Answer 2

Answer:

So, permutations of four different letters are to be explored such there is at least one vowel.

Now, four letter word can be formed in two patterns.

Pattern-1: Using three consonants and one vowel. Three consonants can be chosen in (4C3) ways = 4 ways and one vowel can be chosen in (2C1) ways = 2 ways; and the four chosen letters can be permuted in (4!) ways = 24 ways. So, as per Pattern-1; there are (4 * 2 * 24) = 192 permutations.

Pattern-2: Using two consonants and two vowels. Two consonants can be chosen in (4C2) ways = 6 ways and two vowels can be chosen in (2C2) way = 1 way; and four chosen letters can be permuted in (4!) ways = 24 ways. So, as per Pattern-2; there are (6 * 1 * 24) = 144 permutations.

Thus, combining Pattern-1 and Pattern-2; there shall be (192 + 144) = 336 permutations.

Step-by-step explanation:

Brainliest