Given a deck of 52 cards
There are 4 Ace cards in a deck of 52 cards.
According to question, we need to select 1 Ace card out the 4 Ace cards
Number of ways to select 1 Ace from 4 Ace cards is 4C1
More 4 cards are to be selected now from 48 cards (52 cards – 4 Ace cards)
Number of ways to select 4 cards from 48 cards is 48C4
\( \dfrac{4!}{1!(4-11)!}\times \dfrac{48!}{4!(48-4)!}=\dfrac{4!}{1!\times 3!}\times \dfrac{48!}{4!\times 44!}\)
= \( \dfrac{4\times 3!}{1!\times 3!}\times \dfrac{48\times 47\times 46\times 45\times 44!}{4!\times 44!}\)
= \( \dfrac{4}{1}\times \dfrac{4669920}{24}\)
= \( 4\times 194580\)
= 778320.
Number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination 778320.
Answered by Abhisek | 1 year agoHow many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if
(i) 4 letters are used at a time
(ii) all letters are used at a time
(iii) all letters are used but first letter is a vowel ?
There are 10 persons named P1, P2, P3 …, P10. Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?