Question
Find the number of ways of arranging the letters of the word “MATERIAL” such that all the vowels in the word are to come together?
Answer: Option B
IN THE WORD, “MATERIAL” THERE ARE THREE VOWELS A, I, E.
IF ALL THE VOWELS ARE TOGETHER, THE ARRANGEMENT IS MTRL’AAEI’.
CONSIDER AAEI AS ONE UNIT. THE ARRANGEMENT IS AS FOLLOWS.
M T R L A A E I
THE ABOVE 5 ITEMS CAN BE ARRANGED IN 5! WAYS AND AAEI CAN BE ARRANGED AMONG THEMSELVES IN 4!/2! WAYS.
NUMBER OF REQUIRED WAYS OF ARRANGING THE ABOVE LETTERS = 5! * 4!/2!
= (120 * 24)/2 = 1440 WAYS.
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IN THE WORD, “MATERIAL” THERE ARE THREE VOWELS A, I, E.
IF ALL THE VOWELS ARE TOGETHER, THE ARRANGEMENT IS MTRL’AAEI’.
CONSIDER AAEI AS ONE UNIT. THE ARRANGEMENT IS AS FOLLOWS.
M T R L A A E I
THE ABOVE 5 ITEMS CAN BE ARRANGED IN 5! WAYS AND AAEI CAN BE ARRANGED AMONG THEMSELVES IN 4!/2! WAYS.
NUMBER OF REQUIRED WAYS OF ARRANGING THE ABOVE LETTERS = 5! * 4!/2!
= (120 * 24)/2 = 1440 WAYS.
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