Quarter-3-Lesson-2-Finding-the-value-of-n-and-r-in-permutations-edited.pptx

Quarter-3-Lesson-2-Finding-the-value-of-n-and-r-in-permutations-edited.pptx

1. Finding the value of n and r in permutation MELC Quarter 3 Week 1

2. Review of Formulas:

3. Find the permutations of numbers 1 to 10 if 5 numbers are taken at a time. Given:     Formula:          

4.   Given:           Solution:                                

5.   Given:           Solution:                              

6.   Given:           Solution:                              

7. 720   Given:           Solution:     n!                     n!       Cross multiply Cancel all factorial notation Convert 720 to factorial form Distribute 6 Transpose n to the left Simplify Cancel 5 to solve for n

8.   Given:           Solution:     n!                 15   15   n!       Cross multiply Cancel all factorial notation Convert 60 to factorial form Distribute 5 Transpose n to the left, -15 to the right Simplify Cancel 3 to solve for n n!2!  

9. 04   Given:           Solution:     n!     504     504         n!       Cross multiply Cancel all factorial notation Convert 504 to factorial form Distribute 9 Transpose n to the left, -27 to the right Simplify Cancel 3 to solve for n n!6!   Eliminate denominator

10. 024   Given:           Solution:     n!     3024     3024         n!       Cross multiply Cancel all factorial notation Convert 3024 to factorial form Distribute 9 Transpose n to the left, -36 to the right Simplify Cancel 4 to solve for n n!5!  

11. Solve Problems Involving Permutations MELC Quarter 3 Week 1

12. GEANHS will conduct a beauty pageant “Search for Binibining Sipnayan ”. For this year, 10 students join on the said event. In how many ways can 3 rd runner up, 2nd runner up, 1st runner up and the title holder be selected? Given:     Formula:        

13. How many arrangements can be made from the word TAGAYTAY ? Given:         Formula:        

14. In how many ways can 5 different plants be planted in a circle? Given: n = 5 Solution:        

15. A bracelet needs 10 chains of different colors. In how many ways can the chains be arranged or joined to form a bracelet? Given: n = 10 Solution:    

16. There are 4 copies of Mathematics book, 5 copies of English book and 3 copies of Science book. In how many ways can they be arranged on a shelf? Given:       Formula:          

17. How many 4-digit numbers can be formed from the digits 1, 3, 5, 6, 8 & 9 if (a) if repetition is allowed (b) repetition is not allowed. 6 6 6     1296 possible ways   6   (a) Given:     Formula:         (b)

18. There are 4 different Math books and 5 different Science books. In how many ways can the books be arranged on a shelf if (a) there are no restrictions? (b) books of the same subjects must be placed together. (c) if they must be placed alternately?       4! 5! 2!     5, 760 possible ways   5 4 4     1296 possible ways   3   3 2     2   1 1    

19. There are 12 people in a dinner gathering. In how many ways can the host (1 of the 12) arrange his guest in the dining table if (a) they can sit on any of the chairs? (b) 3 people insist on sitting beside each other (c) 2 people refuse to sit beside each other       (12-3)! 3!   2, 177, 280 possible ways     32, 659, 200 possible ways   (12 - 2)!     2! (12 – 1)! 7,257,600