Find the R Th Term in the Binomial Expansion $( z + y ) ^ { n }$

question 131

Multiple Choice

Find the r th term in the binomial expansion. $( z + y ) ^ { n }$

• A) \(\frac { n ! } { ( n - r ) ! r ! } z ^ { n - r } y ^ { r }\)
• B) \(\quad \frac { n ! } { ( n - r ) ! r ! } z ^ { n - r + 1 } y ^ { r - 1 }\)
• C) \(\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r } y ^ { r - 1 }\)
• D)\(\frac { n ! } { ( n + r - 1 ) ! ( r + 1 ) ! } z ^ { n + r - 1 } y ^ { r + 1 }\)
• E)
• \(\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r + 1 } y ^ { r - 1 }\)

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Definitions:

Daytime Sleepiness

A condition characterized by an increased tendency to fall asleep during the day, often related to inadequate or disturbed nighttime sleep.

Sleep Cycle

The progression through various stages of sleep, including REM and non-REM phases, that occurs several times throughout the night.

Sleep

A naturally recurring state of mind and body, characterized by altered consciousness, relatively inhibited sensory activity, and inhibition of nearly all voluntary muscles.

Rest

A period of relaxation, sleep, or inactivity, especially after a period of work or strenuous activity, allowing for recovery and rejuvenation.