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How many words with out without meaning, can be formed by using all the letters of the word "TRIANGLE"?

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From a committee of 8 persons, in how many ways can we choose a Chairman and a Vice-chairman, assuming one person can not hold more than one post?

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In a monthly test, the teacher decides that there will be 3 questions, one from each of the exercise 1, 2 &3 of the text book. If there are 10 questions in Exercise 1, 6 questions in Exercise 2, 9 questions in Exercise 3.

In how many ways can three questions be selected?

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How many 4-digit numbers with each digit even can be formed if:

(i) repetition of digits is not allowed

(ii) repetition of digits is allowed

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Hold a class discussion where students can share instances where permutations are used in real life, such as in password generation, seating arrangements, etc. This will help them connect the concept with real-world applications.

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Students will write and illustrate a short story or comic book that incorporates permutation scenarios. This activity encourages creative thinking and application of permutations in storytelling.

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Challenge students to design and solve their own permutation puzzles. This fosters creativity and deepens their understanding of permutation concepts.

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8 men & 4 women in a row, so that women occupy the even places. how many such arrangements are possible?

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If each user on a computer system has a password which is eight characters long where each character is an upper case letter or a digit.

Each password must contain at least one digit. How many password are possible.

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When GENERATE button is clicked, System generates the 4 digit pin number automatically.

How many possible PIN numbers can a system generate?

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In how many ways can a group of 8 friends having different heights stand in a row for a group photograph if

(i) they stand in ascending order of their heights (from left to right)

(ii) the tallest and the shortest should not stand together.

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Find the number of arrangements of the letters of the word FRAGILE.

In how many of these arrangements

(i) do all the vowels occur together.

(ii) do all the vowels occur together and all the consonants occur together.

(iii) do all the vowels never occur together.