Trainings

The table contains tennis training schedule for Saturday's younger students during the winter indoor season. Before the start of the summer season is preparing a new training schedule. Tomas Kucera will be able to practice only in the morning, sisters Kovacova will have to train in any order only one after one. Other students meet all times.

How many different schedules tennis training under these conditions can be created for these eight students?


9:00 to 9:55 Jana Abrahámová
10:00 to 10:55 Tomas Kucera
11:00 to 11:55 Beata Gross
12:00 to 12:55 Dana Ihringová
13:00 to 13:55 Ingrid Hájková
14:00 to 14:55 Katarina Kovacova
15:00 to 15:55 Zuzana Kovacova
16:00 to 16:55 Peter Valent


Result

x =  4080

Solution:

Program in PHP:
for($a=1;$a<=8;$a++) {
    for($b=1;$b<=8;$b++) {
        for($c=1;$c<=8;$c++) {
            for($d=1;$d<=8;$d++) {
                for($e=1;$e<=8;$e++) {
                    for($f=1;$f<=8 ;$f++) {
                        for($g=1;$g<=8;$g++) {
                            for($h=1;$h<=8;$h++) {

if($a != 1 && $b != 1 && $c != 1)
{
    continue;
}

if($a==2 && $b!=3 || $b==2 && $c!=3
    || $c==2 && $d!=3 || $d==2 && $e!=3 ||
    $e==2 && $f!=3 || $f==2 && $g!=3 ||
    $g==2 && $h!=3)
{
    continue;
}

$aa = array($a, $b, $c, $d, $e, $f, $g, $h);
if(count($aa) != count(array_unique($aa)))
{
    continue;
}
$cnt++;

}}}}}}}}
echo 'count of permutations: '.$cnt;

Solution in text x =







Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




To solve this verbal math problem are needed these knowledge from mathematics:

See also our permutations calculator. See also our variations calculator. Would you like to compute count of combinations?

Next similar examples:

  1. Variations
    pantagram 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.
  2. PIN - codes
    pin How many five-digit PIN - code can we create using the even numbers?
  3. Neighborhood
    glasses_1 I have 7 cups: 1 2 3 4 5 6 7. How many opportunities of standings cups are there if 1 and 2 are always neighborhood?
  4. Toys
    toys 3 children pulled 12 different toys from a box. Many ways can be divided toys so that each children had at least one toy?
  5. Election 4
    vote_1 In a certain election there are 3 candidates for president 5 for secretory and 2 for tresurer. Find how many ways the election may (turn out/held).
  6. Olympics metals
    olympics In how many ways can be win six athletes medal positions in the Olympics? Metal color matters.
  7. Medals
    medails In how many ways can be divided gold, silver and bronze medal among 21 contestant?
  8. Tokens
    kamene In the non-transparent bags are red, white, yellow, blue tokens. We 3times pull one tokens and again returned it, write down all possibilities.
  9. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  10. Digits
    numbers2_18 How many natural numbers greater than 4000 which are formed from the numbers 0,1,3,7,9 with the figures not repeated, B) How many will the number of natural numbers less than 4000 and the numbers can be repeated?
  11. Password dalibor
    lock Kamila wants to change the password daliborZ by a) two consonants exchanged between themselves, b) changes one little vowel to such same great vowel c) makes this two changes. How many opportunities have a choice?
  12. A jackpot
    jackpot3 How many times must I play this jackpot to win? A jackpot of seven games having (1 X 2), i. E. , home win or away win.
  13. Numbers
    numbers_3 How many different 7 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2,3,4,5,6?
  14. Chess
    sachovnica How many ways can select 4 fields on classic chess board with 64 fields, so that fields don't has the same color?
  15. Word MATEMATIKA
    math_1 How many words can be created from the word MATEMATIKA by changing the order of the letters, regardless of whether or not the words are meaningful?
  16. Tricolors
    Flag_of_the_Netherlands.svg From the colors - red, blue, green, black and white, create all possible tricolors.
  17. Digits
    numbers_48 How many five-digit numbers can be written from numbers 0.3,4, 5, 7 that is divided by 10 and if digits can be repeated.