Q. 265.0( 2 Votes )
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
Answer :
Given that 5 cards are drawn out of 52 cards. We know that there are 4 aces present in a deck of 52 cards.
We need to find the no. of ways of drawing 5 cards with exactly one ace out of a deck of 52 cards.
Let us assume the no. of ways of drawing cards be N.
⇒ N = (Drawing 1 ace out of 4 aces) × (Drawing 4 cards out of remaining 48 cards)
⇒ N = (4C1) × (48C4)
We know that 
,
And also n! = (n)(n – 1)......2.1
⇒ 
⇒ 
⇒ 
⇒ N = 4 × 194580
⇒ N = 778320
∴ The no. of ways of drawing 5 cards with exactly one ace is 778320.
Rate this question :
Permutations & Combinations | Analyze your learningFREE Class
Challenging Quiz on P&C | Test Yourself55 mins
Understand Permutations like never before60 mins
Check Your progress Part 2| Interactive Quiz: Permutation & Combination54 mins
Interactive Quiz on Combinations50 mins
Lecture on Combinations49 mins
Interactive Quiz on Division and distribution of objects17 mins
Division and distribution of objects58 mins
Interactive Quiz on Combinations-0253 mins
Circular permutations61 mins
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
RD Sharma - MathematicsA 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 :
at least 3 girls?
RD Sharma - MathematicsHow many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if
4 letters are used at a time
RD Sharma - MathematicsA parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
RD Sharma - MathematicsHow many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if
all letters are used at a time
RD Sharma - MathematicsOut of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines (ii) triangles can be formed by joining them?
RD Sharma - Mathematics