Advertisements
Advertisements
Question
Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?
Advertisements
Solution
There are 4 kings in the deck of cards.
So, we are left with 48 cards out of 52.
∴ Required combination =\[{}^{48} C_1 \times^4 C_4 + {}^{48} C_2 \times^4 C_3 + {}^{48} C_3 \times^4 C_2 + {}^{48} C_4 \times^4 C_1 \]
\[= 48 + 4512 + 103776 + 778320\]
\[ = 886656\]
APPEARS IN
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
If nC10 = nC12, find 23Cn.
If 18Cx = 18Cx + 2, find x.
If 8Cr − 7C3 = 7C2, find r.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If 16Cr = 16Cr + 2, find rC4.
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
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 (ii) at least one boy and one girl?
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
If 15C3r = 15Cr + 3 , then r is equal to
If mC1 = nC2 , then
If nCr + nCr + 1 = n + 1Cx , then x =
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Find the value of 15C4
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
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 selections be made?
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?
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 no girls
15C8 + 15C9 – 15C6 – 15C7 = ______.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is ______.
