Problem solving ang SHOW SOLUTION
1. How many lottery tickets must be purchased to complete all possible combinations of six numbers, each with a possibility of being from 1 to 49?
2. A singer/performer is auditioning for a musical play. If she is required to sing any three of the 7 prepared songs, in how many ways can she make her choice?
Answers
Given : A singer/performer is auditioning for a musical play.
she is required to sing any three of the 7 prepared songs,
To Find : how many ways can she make her choice
Solution:
Total Song = 7
Songs to be sing = 3
3 songs out of 7 can be selected in ⁷C₃ ways
= 35
and 3 songs can be sing in 3! = 6 ways
Hence total number of ways = 35 * 6 = 210
Another method
1st song can be selected in 7 ways
2nd song can be selected in 6 ways
3rd song can be selected in 5 ways
Total Ways = 7 x 6 x 5 = 210
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Step-by-step explanation:
Given
How many lottery tickets must be purchased to complete all possible combinations of six numbers, each with a possibility of being from 1 to 49?
- So the given numbers or elements cannot be repeated.
- So we have n = 49, and r = 6
- So n Cr = n! / r! (n – r)!
- 49 C6 = 49! / 6! (49 – 6)!
- = 49! / 6! x 43!
- = 49 x 48 x 47 x 46 x 45 x 44 / 6 x 5 x 4 x 3 x 2 x 1
- = 13983816
Reference link will be
https://brainly.ph/question/12730068