Question

COMBINATIONS

Do the following problems using combinations.

1) How many different 5-player teams can be chosen from eight players?

2) How many 13-card bridge hands can be chosen from a deck of cards?

COMBINATIONS INVOLVING SEVERAL SETS

Following problems involve combinations from several different sets.

1) A club has 4 men, 5 women, 8 boys and 10 girls as members. In how many ways can a group of 2 men, 3 women, 4 boys and 4 girls be chosen?

2) How many 4-letter word sequences consisting of two vowels and two consonants can be made from the letters of the word PHOENIX if no letter is repeated?

Answer 1

SOLUTION-

1.) No of players = 8

Players to be chosen = 5

Hence, Total ways of choosing 5 different players out of 8 players =

2.) A deck of card contains 52 cards.

So ways of choosing a 13-card bridge hand out of a deck of cards =

3.) Men=4, Women=5,Boys=8,Girls=10

Members to be chosen are: 2 Men,3Women,4Boys,4girls.

So possible ways =

4.) 'PHOENIX' HAS THREE VOWELS(O,E,I) AND FOUR CONSONENTS(P,H,N,X)

WE HAVE TO CHOOSE A 4 LETTER SEQUENCE CONTAINING 2 VOWELS AND 2 CONSONENTS WHICH HAVE NO REPETITIONS.

NOW Ways of CHOOSING 2 VOWELS OUT OF 3 =

Ways of choosing 2 CONSONENTS out of 4=

They can order themselves in 4! = 24 ways

Hence, total no of ways = 3*6*24= 432 ways

**Remark**- In case of doubt, comment below.Also like the solution if possible.