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15 coins are tossed , the probability of...

15 coins are tossed , the probability of getting heads will be

A

` (511 ) /( 32768) `

B

` ( 1001 ) /( 32768 ) `

C

` ( 3003 ) /( 32768 ) `

D

` ( 3005 )/( 32768 ) `

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The correct Answer is:
C
` therefore ` Required probability ` = ""^( 15)C _ ( 10 ) (( 1 ) /( 2 ) ) ^( 10) ( ( 1)/ ( 2 ) ) ^( 5 ) `
` = ""^( 15 ) C _ 5 ( 1 ) /( 2 ^ ( 15 ) ) `
` = ( 15 xx 14 xx 13 xx 12 xx 11 ) /( 5 xx 4 xx 3xx 2 xx 1 ) xx ( 1 ) /( 2 ^ ( 15 ) ) `
` = ( 3003 )/( 32768 ) `
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