Math logic

There are 20 children in the group, each two children have a different name. Alena and John are among them. How many ways can we choose 8 children to be among the selected

A) was John
B) was John and Alena
C) at least one was Alena, John
D) maximum one was Alena, John?

Correct result:

a =  50388
b =  18564
c =  75582
d =  196035840

Solution:

$$\begin{gathered} p_1=7!=5040 \\ a=1\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13\mathrm{/}{p}_1=1\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13\mathrm{/}5040=50388 \end{gathered}$$

$$\begin{gathered} p_2=6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=720 \\ b=1\cdot 1\cdot 18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13\mathrm{/}{p}_2=1\cdot 1\cdot 18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13\mathrm{/}720=18564 \end{gathered}$$

$$\begin{gathered} p_3=7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1\cdot 2=10080 \\ c=3\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13\mathrm{/}{p}_3=3\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13\mathrm{/}10080=75582 \end{gathered}$$

$d=2\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13\cdot 12\cdot 11=196035840=1.960358\cdot 10^8$

Try another example

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:

Next similar math problems:

• Blocks
  There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
• Trinity
  How many different triads can be selected from the group 43 students?
• Weekly service
  In the class are 20 pupils. How many opportunities have the teacher if he wants choose two pupils randomly who will weeklies?
• Chords
  How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
• Hockey
  Hockey match ended 8:2. How many different matches could be?
• Fish tank
  A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
• Committees
  How many different committees of 2 people can be formed from a class of 21 students?
• Menu
  On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?
• Commitee
  A class consists of 6 males and 7 females. How many committees of 7 are possible if the committee must consist of 2 males and 5 females?
• 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?
• The confectionery
  The confectionery sold 5 kinds of ice cream. In how many ways can I buy 3 kinds if order of ice creams does not matter?
• Big factorial
  How many zeros end number 116! ?
• Median
  The number of missed hours was recorded in 11 pupils: 5,12,6,8,10,7,5,110,2,5,6. Determine the median.
• A student
  A student is to answer 8 out of 10 questions on the exam. a) find the number n of ways the student can choose 8 out of 10 questions b) find n if the student must answer the first three questions c) How many if he must answer at least 4 of the first 5 ques
• Examination
  The class is 21 students. How many ways can choose two to examination?
• Calculation of CN
  Calculate: ?
• PIN - codes
  How many five-digit PIN - code can we create using the even numbers?