Combination and Factorial Notation and Calculator Problems

1. Without a calculator, evaluate 4!



 2. Use your calculator to evaluate 30!/12!



3. Without a calculator, evaluate . 4. Use your calculator to evaluate = 25C13



5. Without a calculator, simplify . (There should be no factorials in your answer.)





6. Use your calculator to write out the first 7 terms of the sequence: and put your answer in fraction form. To do this in the calculator you go to “LIST”, then “OPS”, then “seq(”. Hit enter, then you need each of the following items with a comma in between each item: the formula, the variable that is changing, the starting value of the variable, the ending value of the variable, the incremental change (how much the variable is increasing between each item in the list, usually equals 1) in the variables value.





7. Use your calculator to evaluate the first 7 partial sums of the sequence in number 6. To do this go to “LIST”, then “OPS”, then “cumSum(”, then hit “ANS” and “)”.





Solutions

  1. 24
  2. 5.537 × 1023
  3. 21
  1. 5,200,300
  2. (n2 - n)/2
  1. seq(3^X/X!, X, 1, 7, 1) = {3 9/2 9/2 27/8 81/40 81/80 243/560}
  2. cumSum(Ans) = {3 7.5 12 15.375 17.4 18.4125 18.84642857} = {3 15/2 12 123/8 87/5 1473/80 5277/280}