determine the number of 5 card selections of a deck of 52 cards if each selection of 5 cards should have exactly one king

ncert cbse chapter 7 permutations miscellaneous exercise

8.determine the number of 5 card selections of a deck of 52 cards if each selection of 5 cards should have exactly one king

First select the king. Since there are four kings, this can be done in

C(4,1) ways.

Now after removing the 4 kings there are 52-4 = 48 cards which will be used to select the remaining 4 non king cards which can be done in C(48,4)

Answer = C(4,1) * C(48,4)

9. It is required to seat 5 men and 4 ladies in a row so that the ladies occupy the even positions. How many such arrangements are possible.

The required arrangement is like

M W M W M W M W M

The men can be arranged in ( 5! ) =120 ways

Now arrange the ladies in their even positions in (4!) = 24 ways

Answer = 120*24 =2880 ways

10. In a class of  25 students, 10 are to be chosen  for an excursion party. There are 3 students who decide that either all of them will join or none of them will go. In how many ways can the party be chosen.

First possibility

All 3 of the friends join the party

Now all we have to do is to select the remaining 7 participants using the remaining (25-3)=22 students in C(22,7) ways

OR

Second possibility

None of the three friends join the party

Now we have to select the entire 10 participants using the remaining (25-3)=22 students in C(22,10) ways

Answer  = C(22,7) + C(22,10)

ncert cbse 11th mathematics chapter  7 permutations exercise 7.3

11.In how many ways can the letters of the word PERMUTATIONS be arranged if

i)words start with P and end with S

ii)vowels are all together

iii)there are always 4 letters between P and S

solution

ncert cbse 11th mathematics chapter  7 permutations miscellaneous exercise

1.How many words each of 2 vowels and 3 consonants can be formed using the letters of the word DAUGHTER

solution

2. How many words of can be formed using all the letters of the word

 EQUATION  so that the vowels and consonants occur together?

solution

4. If the different permutations of the word EXAMINATION are arranged in a dictionary how many words are there in this list before the first word starting with E

solution

6.How many 6 digit numbers can be formed using 0,1,3,5,7,9 which are divisible by 10 and no digit is repeated?

solution

6.The english alphabet has 5 vowels and 21 consonants. How many words with 2 different vowels and 2 different consonants can be formed

solution

7. In an examination  a question paper consists of two parts containing 5 and 7 questions respectively. A  student is required to answer 8 questions in all selecting atleast 3  from each part.  In how many ways can a student select the questions?

solution

8.determine the number of 5 card selections of a deck of 52 cards if each selection of 5 cards should have exactly one king

solution

9. It is required to seat 5 men and 4 ladies in a row so that the ladies occupy the even positions. How many such arrangements are possible.

solution

10. In a class of  25 students, 10 are to be chosen  for an excursion party. There are 3 students who decide that either all of them will join or none of them will go. In how many ways can the party be chosen.

solution

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