Advertisements
Advertisements
प्रश्न
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
Advertisements
उत्तर
In a deck of 52 cards, there are 4 aces. A combination of 5 cards have to be made in which there is exactly one ace.
Then, one ace can be selected in 4C1 ways and the remaining 4 cards can be selected out of the 48 cards in 48C4 ways.
Thus, by multiplication principle, required number of 5 card combinations
= `""^48C_4 xx ""^4C_1 = (48!)/(4! xx 44!) xx (4!)/(1! xx 3!)`
= `(48 xx 47 xx 46 xx 45)/(4 xx 3 xx 2 xx 1) xx 4`
= 778320
APPEARS IN
संबंधित प्रश्न
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
From 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 join. In how many ways can the excursion party be chosen?
Compute:
(i)\[\frac{30!}{28!}\]
How many 3-digit numbers are there, with distinct digits, with each digit odd?
If nC10 = nC12, find 23Cn.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is excluded.
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has(iii) at least 3 girls?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
There are 8 doctors and 4 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.
Find the value of 15C4 + 15C5
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
15C8 + 15C9 – 15C6 – 15C7 = ______.
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
