Untitled

• permutation - order and arrangement matter
• Permutation or Combination: if there are 10 people and only 6 chairs are available, in how many ways can they be seated?

  Permutation
• Combination - order and arrangement DOES NOT matter
• Permutation formula

  nPr = n!/(n-r)!
• Permutation of n DISTINCT OBJECTS

  nPr= n!/(n-r)!
• Permutation of n NON-DISTINCT objects: nPr=n!/r1!r2!r3!...rk
• PERMUTATION or COMBINATION: How many different sets of 5 cards each can be formed from a 52 deck of cards

  COMBINATION
• if n = r

  nPn = n!
• CIRCULAR PERMUTATION

  Pn= (n-1)!
• PERMUTATION OR COMBINATION: In how many ways can 5 English books and 4 Math books be placed on a shelf if the books of the same subject are to be together?

  PERMUTATION
• 9P4 =

  3024
• 9C3 =

  84
• 10P5 =

  30240
• Suppose each license plate in a certain state has one digit, followed by four letters, followed by one digit. The letters F, O, S, and X and the digit 0 are not used. So, there are 22 letters and 9 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format?

  18974736
• Amy is choosing a 3-letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?

  60
• Arithmetic Sequence Formula

  an = a + (n-1)d
• Sum of Arithmetic Sequence(formula)

  Sn = (n/2) [2a + (n - 1)d]
• How to find the difference in Arithmetic Sequence?

  d = an - a.
• (Fibonacci or Harmonic?) 1,1,2,3,5,8,13...

  Fibonacci
• (Fibonacci or Harmonic) 1/4, 1/7, 1/10, 1/13, 1/16...

  Harmonic
• Arithmetic Sequence: Find the next two terms. 31, 24, 17...

  10, 3
• Find the 60th term of the following arithmetic sequence: 3,11,19,17...

  475
• The 9th term is equal to -5, and the 29th term is equal to 55. Find the 73rd term.

  187
• Geometric Sequence: -7, 14, -28, __, __?

  -56, 112
• Geometric Sequence Formula

  an=a1(r)^(n-1)
• Sum of Geometric Sequence

  a1(1 - r^n) / (1 - r)