find n and r if ncr-1 :ncr : ncr+1 = 14 : 8 : 3
Answers
Step-by-step explanation:
find n and r if ncr-1 :ncr : ncr+1 = 14 : 8 : 3
The value of n is 10 and r is 7 in the given combination ratio expression.
Combination Calculation :
- Combinations are the count of the number of ways of selection of 'r' items from a given set of 'n' items ( each unique )
- It is denoted using subscript and superscript :
- The formula for it is :
Using the formula in the expansion of the given ratio equation :
Equation 1: Comparing Ratios 1 and 2 :
Divide the quantities of count 1 and 2 to get the ratio of 14 : 8.
Equation 2: Comparing Ratios 2 and 3 :
Divide the quantities of count 2 and 3 to get the ratio of 8 : 3.
Solving the two equations and 2 variables system using the elimination method :
We do ( Equation1 + 2*Equation2 ) to eliminate the variable r.
Using the value of 'n' to find the value of 'r' :
Hence, the value of n and r is 10 and 7 respectively.
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