Question

Seven cards are drawn from an ordinary deck. In how many ways is it possible to draw ​(b) only 8​'s, ​'s and ​(c) no ​'s, ​'s and ​(d) exactly 2 or ​; ​(e) spades and ​hearts? ​(a) Number of ways to draw only ​'s ​= 0 ​(b) Number of ways to draw only ​'s, ​'s, and ​'s ​= 924 ​(c) Number of ways to draw no ​'s, ​'s, and ​'s ​= 3838380 ​(d) Number of ways to draw exactly 2 s or s ​= 3,801,028 ​(e) Number of ways to draw spades and hearts​ = 55770 Question is complete. Tap on the red indicators to see incorrect answers.

Answer 1

Complete question :

Seven cards are drawn from an ordinary deck. In how mnat ways is it possible to draw (a) only 5s (b)only 8s, 9s, and 10s, (c) no 8s, 9s, and 10s (d) exactly 2 jacks or kings, (e) 5 spades and 2 hearts?

Answer:

0; 792 ; 100396 ; 30408224 ; 18643560 ;

Explanation:

Number of cards in a deck = 52

Number of cards to be drawn = 7

Using combination:

nCr = n! ÷ (n-r)!r!

A.)

Number of 5's in a deck = 4

4C7 = 0

(B.)

only 8s, 9s, and 10s,

Number of 8, 9 and 10's = 4 *3 = 12

12C7 = 12! ÷ 5!7! = 792

(C)

no 8s, 9s, and 10s ;

Number of cards to select from = 52 - (3(4)) = 40C7 = 18643560

(D)

exactly 2 jacks or kings,

Number of jack or king in deck = 8 ; other 5 could be any of the rest : (52 - 8) = 44

8C2 * 44C5 = 28 * 1086008 = 30408224

(e) 5 spades and 2 hearts?

Number of spades = 13

Number of hearts = 13

13C5 * 13C2

1287 * 78 = 100396