Question 14 and 15, Exercise 6.2
Solutions of Question 14 and 15 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.
Question 14
How many $3$ letters word (with or without meaning) can be formed out of the letter of the word ENGLISH, if the repetition of the letter os not allowed.
Solution.
Total letters of given word $=7$
No. of letters we can use to make words $=3$
No. of arrangements of 3 letters out of 7 is $={ }^{7} P_{3}=\dfrac{7!}{4!}=210$
Question 15
Fatima wants to arrange $5$ Mathematics, $3$ English and $2$ Urdu books on book shelf. If the books on the same subjects are togather, find all possibile arrangements.
Solution.
To find these arrangement, we treat all books on one subject as one element.
so we have total 3 -elements to arrange on book self.
Possible arrangements of $3$ subjects on shelf $=31=6$
Total possibilities $=(5!\times 3!\times 2!) \times 31=8640$
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