Given word is: TRIANGLE Consonants are: T, R, N, G, L Vowels are: I, A, E Show
Since we have to form words in such a way that no two vowels are together, we first arrange consonants. Five consonants can be arranged in 5! ways.
Permutation is known as the process of organizing the group, body, or numbers in order, selecting the body or numbers from the set, is known as combinations in such a way that the order of the number does not matter. In mathematics, permutation is also known as the process of organizing a group in which all the members of a group are arranged into some sequence or order. The process of permuting is known as the repositioning of its components if the group is already arranged. Permutations take place, in almost every area of mathematics. They mostly appear when different commands on certain limited sets are considered. Permutation Formula In permutation r things are picked from a group of n things without any replacement. In this order of picking matter.
Combination A combination is a function of selecting the number from a set, such that (not like permutation) the order of choice doesn’t matter. In smaller cases, it is conceivable to count the number of combinations. The combination is known as the merging of n things taken k at a time without repetition. In combination, the order doesn’t matter you can select the items in any order. To those combinations in which re-occurrence is allowed, the terms k-selection or k-combination with replication are frequently used. Combination Formula In combination r things are picked from a set of n things and where the order of picking does not matter.
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How many words can be formed from the letters of the word TRIANGLE so that consonants occur together?The total number of words that can be formed using all the 8 letters of the word ' TRIANGLE ' is P(8, 8) = 8 ! = 40320. We have given the word TRIANGLE. Now, TRIANGLE word consist of 8 alphabets, including 3 vowels (A, E, I ) and 5 consonants ( T, R, N, G, L ).
How many vowels does a TRIANGLE have?Now, the given word is TRIANGLE in which there are 3 vowels I, A, E with total letters of 8.
How many ways can the letters of the word TRIANGLE be arranged?How many ways can the letters of the word TRIANGLE be arranged? Solution: Here there are a total of eight choices for the first letter, seven for the second, six for the third, and so on. By the multiplication principle we multiply for a total of 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 8! = 40,320 different ways.
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