Question

Six fair coins are tossed simultaneously. Number of ways in which atmost three of the coins turn up as heads in a definite order, is

• A. $32$
• B. $41$
• C. $42$
• D. $6$

Answer 1

Answer: (C)

$42$

According to question

The outcome in which at most $3$ coin turns us as heads

i.e

$0$ coins turn heads

$1$ coins turn heads

$2$ coins turn heads

$3$ coins turn heads

Number of outcomes in which $0$ coins turn heads is ${}^6{C}_0=1$

Number of outcomes in which $1$ coins turn heads is ${}^6{C}_1=6$

Number of outcomes in which $0$ coins turn heads is ${}^6{C}_2=15$

Number of outcomes in which $0$ coins turn heads is ${}^6{C}_3=20$

So, Total number out outcomes $=1+6+15+20=42$outcomes