Question

Find the number n of distinct permutations that can be formed from all the letters of each word: a)THOSE ; b) UNUSUAL ; c) SOCIOLOGICAL ; d) BENZENE

Answer 1

To find the number of distinct permutations that can be formed from all the letters of a word, you can use the concept of factorials. Simply calculate the factorial of the number of distinct letters in the word to get the number of distinct permutations.

Step-by-step explanation:

To find the number of distinct permutations that can be formed from all the letters of a word, you can use the concept of factorials. The factorial of a number n, denoted as n!, is the product of all positive integers less than or equal to n.

a) For the word 'THOSE', there are 5 distinct letters. So, the number of distinct permutations is 5! = 5 x 4 x 3 x 2 x 1 = 120.

b) For the word 'UNUSUAL', there are 7 distinct letters. So, the number of distinct permutations is 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.

c) For the word 'SOCIOLOGICAL', there are 12 distinct letters. So, the number of distinct permutations is 12! = 12 x 11 x 10 x 9 x ... x 2 x 1 = 479,001,600.

d) For the word 'BENZENE', there are 7 distinct letters. So, the number of distinct permutations is 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.

Answer 2

The number of distinct permutations for words THOSE, UNUSUAL, SOCIOLOGICAL, and BENZENE are 120, 5040, 479,001,600, and 5040, respectively.

Step-by-step explanation:

When finding the number of distinct permutations that can be formed from a word, we use the concept of factorial. The factorial of a number is the product of all positive integers less than or equal to that number.

a) For the word THOSE, there are 5 distinct letters. So, the number of permutations is 5! = 5*4*3*2*1 = 120.

b) For the word UNUSUAL, there are 7 distinct letters. So, the number of permutations is 7! = 7*6*5*4*3*2*1 = 5040.

c) For the word SOCIOLOGICAL, there are 12 distinct letters. So, the number of permutations is 12! = 12*11*10*9*8*7*6*5*4*3*2*1 = 479,001,600.

d) For the word BENZENE, there are 7 distinct letters. So, the number of permutations is 7! = 7*6*5*4*3*2*1 = 5040.