 Hi and welcome to the session. I'm Karika and I'm going to help you to solve the following question. A question says how many words with or without meaning can be made from the letters of the word Monday. Assuming that no letter is repeated if first part is four letters are used at a time, second part is all letters are used at a time and third part is all letters are used but first letter is a bubble. Let's now begin with the solution. In the first part we have to find number of words which can be made from the letters of the word Monday by using four letters at a time. There are six letters in the word Monday and these six letters are m o n d a and y. Since each letter is different and each letter has to be used only once, no repetition is allowed and four letters have to be taken at a time. Therefore number of words formed with four letters of the word Monday. The mutations of n different objects taken are at a time and the objects do not repeat as n p r. Here six different letters, mutations of six different letters taken four at a time minus four factorial and this is equal to six factorial upon. The six factorial can be written as six into five into four into three into two factorial. So we have six into five into four into three into two factorial upon two factorial. We can cancel two factorial from both numerator and denominator. So we are left into three. So 360 is our required only once. It's also given that no repetition is allowed. So number of permutations of six different letters taken all at a time is equal to and r is also equal to six. So six to six is equal to six five to six factorial and this is equal to upon zero factorial. Now six factorial is equal to six into five into four into three into two into one into zero factorial upon zero factorial is equal to six into five into four into three into two into one into zero factorial upon zero factorial. Canceling zero factorial from both numerator and denominator we are left with six into five into four into three into two into one. Unsimplifying it we get seven twenty. Hence our required answer is seven twenty. This completes the second part. Let's now move on to the third post but first letter is a bobble. Letters of the word Monday are using all letters at a time but first letter is a bobble. Commutations p is NPR. Here in different objects are five different letters as I've taken at a time and we know that repetition is not allowed. So number of permutations of rest of five different letters taken all at a time is equal to five p five. We know that is equal to n factorial and r is also equal to five. So five p five is equal to five factorial upon five minus five factorial and this is equal to five factorial upon zero factorial. Now five factorial is equal to five into four into three into two into one into zero factorial. We can cancel zero factorial from both numerator and denominator. So we are left with five into four into three into two into one. Unsimplifying it we get one twenty. Two vowels in the word and these two vowels are O number of rotations taken one at a time is equal to p one and this p one is equal to two factorial upon two minus one factorial. This is equal to two factorial upon one factorial of two factorial is equal to two into One factorial so we have two into one factorial upon one factorial. You can cancel one factorial from both numerator and denominator, so we are left with 2. Therefore, by the multiplication principle, total number of words is equal to number of permutations of 5 different letters taken all at a time that is 120 into number of permutations of 2 vowels taken 1 at a time that is 2. 120 into 2 is 240, hence a required answer is 240. This completes the third part. Bye and take care.