How many different words can be formed with the letters of the word DIPAWALI? In how many of these
(a) P and D are never together?
(b) Vowels are always together?
Answers
Answer:
(a) 7560
(b) 720
Step-by-step explanation:
HI,
Given word is DIPAWALI
There are 6 Distinct letters of the given word, wit A and I each
repeating twice.
So, total ways of arranging 8 letters with 2 letters repeating twice are
8!/2!2! =10080
(a) If P and D are never together, number of ways of such arrangement
are Total number of ways - Number of ways in which P and D are
together.
Number of ways in which both P and D are together are
Lets treat PD as 1, then number of ways of arranging 5 Distinct letters
of the given word, wit A and I each repeating twice.
So, total ways of arranging 7 letters with 2 letters repeating twice are
7!/2!2! =1260.
But P and D can interchange their positions between themselves,
which could happen in 2 different ways, hence total number of ways
are 126*2! = 2520 ways.
Number of ways in which P and D are together are 2520.
So, total number of ways in which P and D are never together are
10080 - 2520
= 7560
(b) In the word DIPAWALI, the vowels are 2 A's and 2 I's
If we treat all 4 vowels as 1 and the rest 4 , so total there are 5 distinct
letters which can be arranged in 5! ways. But thee 4 vowels can be
permuted between themselves in 4!/2!2! ways = 6. So, total number
of ways in which all vowels come together are
5!*6 = 720.
Hope, it helps !
Answer:
Step-by-step explanation:
Answer:
(a) 7560
(b) 720
Step-by-step explanation:
HI,
Given word is DIPAWALI
There are 6 Distinct letters of the given word, wit A and I each
repeating twice.
So, total ways of arranging 8 letters with 2 letters repeating twice are
8!/2!2! =10080
(a) If P and D are never together, number of ways of such arrangement
are Total number of ways - Number of ways in which P and D are
together.
Number of ways in which both P and D are together are
Lets treat PD as 1, then number of ways of arranging 5 Distinct letters
of the given word, wit A and I each repeating twice.
So, total ways of arranging 7 letters with 2 letters repeating twice are
7!/2!2! =1260.
But P and D can interchange their positions between themselves,
which could happen in 2 different ways, hence total number of ways
are 126*2! = 2520 ways.
Number of ways in which P and D are together are 2520.
So, total number of ways in which P and D are never together are
10080 - 2520
= 7560
(b) In the word DIPAWALI, the vowels are 2 A's and 2 I's
If we treat all 4 vowels as 1 and the rest 4 , so total there are 5 distinct
letters which can be arranged in 5! ways. But thee 4 vowels can be
permuted between themselves in 4!/2!2! ways = 6. So, total number
of ways in which all vowels come together are
5!*6 = 720.
Hope, it helps !