Variations

Determine the number of items when the count of variations of fourth class without repeating is 42 times larger than the count of variations of third class without repetition.

Correct result:

n =  45

Solution:

$$\begin{gathered} V_4(n)=42\cdot V_3(n) \\ n(n-1)(n-2)(n-3)=42\cdot n(n-1)(n-2) \\ (n-3)=42 \\ n=42+3=45 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Variations 4/2
  Determine the number of items when the count of variations of fourth class without repeating is 600 times larger than the count of variations of second class without repetition.
• Three-digit numbers
  How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)?
• Variations 3rd class
  From how many elements we can create 13,800 variations 3rd class without repeating?
• First class
  The shipment contains 40 items. 36 are first grade, 4 are defective. How many ways can select 5 items, so that it is no more than one defective?
• Combinations
  From how many elements we can create 990 combinations 2nd class without repeating?
• Combinations
  How many elements can form six times more combinations fourth class than combination of the second class?
• Three-digit
  How many three-digit natural numbers is greater than 321 if no digit in number repeated?
• A three-digit numbers
  Determine the total number of positive three-digit numbers that contain a digit 6.
• Count of triangles
  Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
• Task of the year
  Determine the number of integers from 1 to 10⁶ with ending four digits 2006.
• Beads
  How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?
• Words
  How many 3 letter "words" are possible using 14 letters of the alphabet? a) n - without repetition b) m - with repetition
• Inverted nine
  In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?
• Five letters
  How many ways can five letters be arranged?
• Two groups
  The group of 10 girls should be divided into two groups with at least 4 girls in each group. How many ways can this be done?
• 2nd class variations
  From how many elements you can create 2450 variations of the second class?
• Prize
  How many ways can be rewarded 9 participants with the first, second and third prize in a sports competition?